Download Anna University B-Tech EEE 7th Sem Power System Simulation PSS Lab Manual Question Paper

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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LABORATORY MANUAL
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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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--- Content provided by FirstRanker.com ---

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Name :
Register No. :
Class :

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LABORATORY MANUAL
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VISION

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VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

--- Content provided by FirstRanker.com ---

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

--- Content provided by FirstRanker.com ---

deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

--- Content provided by FirstRanker.com ---

? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

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MISSION
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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

--- Content provided by FirstRanker.com ---

EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

Name :
Register No. :
Class :

LABORATORY MANUAL

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

--- Content provided by FirstRanker.com ---

is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

--- Content provided by FirstRanker.com ---

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

--- Content provided by FirstRanker.com ---

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

--- Content provided by FirstRanker.com ---

ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

--- Content provided by FirstRanker.com ---

? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

--- Content provided by FirstRanker.com ---

? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

--- Content provided by FirstRanker.com ---

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

--- Content provided by FirstRanker.com ---

EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

Name :
Register No. :
Class :

LABORATORY MANUAL

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

--- Content provided by FirstRanker.com ---

is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

--- Content provided by FirstRanker.com ---

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

--- Content provided by FirstRanker.com ---

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

--- Content provided by FirstRanker.com ---

ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

--- Content provided by FirstRanker.com ---

? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

--- Content provided by FirstRanker.com ---

? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

--- Content provided by FirstRanker.com ---

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

--- Content provided by FirstRanker.com ---

education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

--- Content provided by FirstRanker.com ---

To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

--- Content provided by FirstRanker.com ---

broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

--- Content provided by FirstRanker.com ---

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

--- Content provided by FirstRanker.com ---

c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

--- Content provided by FirstRanker.com ---

1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

--- Content provided by FirstRanker.com ---

EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

Name :
Register No. :
Class :

--- Content provided by FirstRanker.com ---

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

--- Content provided by FirstRanker.com ---

is committed to provide highly disciplined, conscientious and

--- Content provided by FirstRanker.com ---

enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

--- Content provided by FirstRanker.com ---

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

--- Content provided by FirstRanker.com ---

DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

--- Content provided by FirstRanker.com ---

? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

--- Content provided by FirstRanker.com ---

communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

--- Content provided by FirstRanker.com ---

enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

--- Content provided by FirstRanker.com ---

3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

--- Content provided by FirstRanker.com ---

students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

--- Content provided by FirstRanker.com ---

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

--- Content provided by FirstRanker.com ---

such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

--- Content provided by FirstRanker.com ---

f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

--- Content provided by FirstRanker.com ---

j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES

--- Content provided by FirstRanker.com ---

COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

--- Content provided by FirstRanker.com ---

LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

--- Content provided by FirstRanker.com ---

5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

--- Content provided by FirstRanker.com ---

10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

--- Content provided by FirstRanker.com ---

3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

--- Content provided by FirstRanker.com ---

7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

--- Content provided by FirstRanker.com ---

10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

--- Content provided by FirstRanker.com ---

13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

--- Content provided by FirstRanker.com ---

DEPARTMENT OF

--- Content provided by FirstRanker.com ---

ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

--- Content provided by FirstRanker.com ---

VII SEMESTER - R 2013

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

Name :
Register No. :

--- Content provided by FirstRanker.com ---

Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

--- Content provided by FirstRanker.com ---

VISION
VISION

--- Content provided by FirstRanker.com ---

is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

--- Content provided by FirstRanker.com ---

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

--- Content provided by FirstRanker.com ---

DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

--- Content provided by FirstRanker.com ---

them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

--- Content provided by FirstRanker.com ---

industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

--- Content provided by FirstRanker.com ---

MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

--- Content provided by FirstRanker.com ---

1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

--- Content provided by FirstRanker.com ---

To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

--- Content provided by FirstRanker.com ---

4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

--- Content provided by FirstRanker.com ---

To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

--- Content provided by FirstRanker.com ---

and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

--- Content provided by FirstRanker.com ---

d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

--- Content provided by FirstRanker.com ---

awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

--- Content provided by FirstRanker.com ---

COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

--- Content provided by FirstRanker.com ---

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

--- Content provided by FirstRanker.com ---

3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

--- Content provided by FirstRanker.com ---

8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

--- Content provided by FirstRanker.com ---

1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

--- Content provided by FirstRanker.com ---

5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

--- Content provided by FirstRanker.com ---

9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

--- Content provided by FirstRanker.com ---

Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

--- Content provided by FirstRanker.com ---

CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

--- Content provided by FirstRanker.com ---

5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

--- Content provided by FirstRanker.com ---

9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

--- Content provided by FirstRanker.com ---

and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

--- Content provided by FirstRanker.com ---

? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

--- Content provided by FirstRanker.com ---

for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

--- Content provided by FirstRanker.com ---

>> quit
(Or)
>>exit
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

--- Content provided by FirstRanker.com ---

?

--- Content provided by FirstRanker.com ---

DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

--- Content provided by FirstRanker.com ---

EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

Name :
Register No. :
Class :

--- Content provided by FirstRanker.com ---

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION

--- Content provided by FirstRanker.com ---

VISION

--- Content provided by FirstRanker.com ---

is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

--- Content provided by FirstRanker.com ---

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

--- Content provided by FirstRanker.com ---

DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

--- Content provided by FirstRanker.com ---

deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

--- Content provided by FirstRanker.com ---

? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

--- Content provided by FirstRanker.com ---

MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals

--- Content provided by FirstRanker.com ---

To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and

--- Content provided by FirstRanker.com ---

training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism

--- Content provided by FirstRanker.com ---

To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,

--- Content provided by FirstRanker.com ---

through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field

--- Content provided by FirstRanker.com ---

b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems

--- Content provided by FirstRanker.com ---

e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility

--- Content provided by FirstRanker.com ---

i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

--- Content provided by FirstRanker.com ---

COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

--- Content provided by FirstRanker.com ---

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.

--- Content provided by FirstRanker.com ---

4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems

--- Content provided by FirstRanker.com ---

9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.

--- Content provided by FirstRanker.com ---

2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.

--- Content provided by FirstRanker.com ---

6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi

--- Content provided by FirstRanker.com ---

machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.

--- Content provided by FirstRanker.com ---

12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

--- Content provided by FirstRanker.com ---

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS

--- Content provided by FirstRanker.com ---

1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26

--- Content provided by FirstRanker.com ---

6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41

--- Content provided by FirstRanker.com ---

10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems

--- Content provided by FirstRanker.com ---

Software required:
MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and

--- Content provided by FirstRanker.com ---

programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.

--- Content provided by FirstRanker.com ---

1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization

--- Content provided by FirstRanker.com ---

? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small

--- Content provided by FirstRanker.com ---

and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit

--- Content provided by FirstRanker.com ---

(Or)
>>exit
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 7

To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,

--- Content provided by FirstRanker.com ---

where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing

--- Content provided by FirstRanker.com ---

them.
M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be

--- Content provided by FirstRanker.com ---

called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace

--- Content provided by FirstRanker.com ---

>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more

--- Content provided by FirstRanker.com ---

generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the

--- Content provided by FirstRanker.com ---

Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators

--- Content provided by FirstRanker.com ---

2. Using transfer functions
3. Using state space equations
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

--- Content provided by FirstRanker.com ---

?

--- Content provided by FirstRanker.com ---

DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

--- Content provided by FirstRanker.com ---

EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

Name :
Register No. :
Class :

--- Content provided by FirstRanker.com ---

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

--- Content provided by FirstRanker.com ---

is committed to provide highly disciplined, conscientious and

--- Content provided by FirstRanker.com ---

enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

--- Content provided by FirstRanker.com ---

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

--- Content provided by FirstRanker.com ---

DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

--- Content provided by FirstRanker.com ---

? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

--- Content provided by FirstRanker.com ---

communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

--- Content provided by FirstRanker.com ---

enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

--- Content provided by FirstRanker.com ---

3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

--- Content provided by FirstRanker.com ---

students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

--- Content provided by FirstRanker.com ---

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

--- Content provided by FirstRanker.com ---

such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

--- Content provided by FirstRanker.com ---

f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

--- Content provided by FirstRanker.com ---

j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES

--- Content provided by FirstRanker.com ---

COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

--- Content provided by FirstRanker.com ---

LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

--- Content provided by FirstRanker.com ---

5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

--- Content provided by FirstRanker.com ---

10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

--- Content provided by FirstRanker.com ---

3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

--- Content provided by FirstRanker.com ---

7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

--- Content provided by FirstRanker.com ---

10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

--- Content provided by FirstRanker.com ---

13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

--- Content provided by FirstRanker.com ---

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

--- Content provided by FirstRanker.com ---

2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

--- Content provided by FirstRanker.com ---

7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

--- Content provided by FirstRanker.com ---

11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

--- Content provided by FirstRanker.com ---

Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

--- Content provided by FirstRanker.com ---

MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

--- Content provided by FirstRanker.com ---

notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

--- Content provided by FirstRanker.com ---

? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

--- Content provided by FirstRanker.com ---

? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

--- Content provided by FirstRanker.com ---

applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

--- Content provided by FirstRanker.com ---

>>exit
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 7

To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

--- Content provided by FirstRanker.com ---

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

--- Content provided by FirstRanker.com ---

M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

--- Content provided by FirstRanker.com ---

ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

--- Content provided by FirstRanker.com ---

These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

--- Content provided by FirstRanker.com ---

be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

--- Content provided by FirstRanker.com ---

of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

--- Content provided by FirstRanker.com ---

3. Using state space equations
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 8

4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

--- Content provided by FirstRanker.com ---

the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

--- Content provided by FirstRanker.com ---

(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

--- Content provided by FirstRanker.com ---

/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

--- Content provided by FirstRanker.com ---

always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

--- Content provided by FirstRanker.com ---

>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

--- Content provided by FirstRanker.com ---

respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

--- Content provided by FirstRanker.com ---

FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

--- Content provided by FirstRanker.com ---

VII SEMESTER - R 2013

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

Name :

--- Content provided by FirstRanker.com ---

Register No. :
Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

--- Content provided by FirstRanker.com ---

VISION
VISION

--- Content provided by FirstRanker.com ---

is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

--- Content provided by FirstRanker.com ---

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and

--- Content provided by FirstRanker.com ---

soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING

--- Content provided by FirstRanker.com ---

To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

--- Content provided by FirstRanker.com ---

? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and

--- Content provided by FirstRanker.com ---

ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

--- Content provided by FirstRanker.com ---

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education

--- Content provided by FirstRanker.com ---

2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables

--- Content provided by FirstRanker.com ---

them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context

--- Content provided by FirstRanker.com ---

5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)

--- Content provided by FirstRanker.com ---

a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical

--- Content provided by FirstRanker.com ---

and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large

--- Content provided by FirstRanker.com ---

h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY

--- Content provided by FirstRanker.com ---

SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines

--- Content provided by FirstRanker.com ---

2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System

--- Content provided by FirstRanker.com ---

7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

--- Content provided by FirstRanker.com ---

1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance

--- Content provided by FirstRanker.com ---

matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.

--- Content provided by FirstRanker.com ---

8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.

--- Content provided by FirstRanker.com ---

11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.

--- Content provided by FirstRanker.com ---

14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS

--- Content provided by FirstRanker.com ---

Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19

--- Content provided by FirstRanker.com ---

4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS

--- Content provided by FirstRanker.com ---

8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58

--- Content provided by FirstRanker.com ---

Mini Project
13 Modeling of FACTS devices using SIMULINK 68
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

Expt. No.1: INTRODUCTION TO MATLAB

--- Content provided by FirstRanker.com ---

Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:

--- Content provided by FirstRanker.com ---

1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and

--- Content provided by FirstRanker.com ---

communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development

--- Content provided by FirstRanker.com ---

? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical

--- Content provided by FirstRanker.com ---

manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:

--- Content provided by FirstRanker.com ---

To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 7

--- Content provided by FirstRanker.com ---

To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.

--- Content provided by FirstRanker.com ---

Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

--- Content provided by FirstRanker.com ---

i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file

--- Content provided by FirstRanker.com ---

M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined

--- Content provided by FirstRanker.com ---

function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.

--- Content provided by FirstRanker.com ---

>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic

--- Content provided by FirstRanker.com ---

equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 8

--- Content provided by FirstRanker.com ---

4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.

--- Content provided by FirstRanker.com ---

>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common

--- Content provided by FirstRanker.com ---

data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.

--- Content provided by FirstRanker.com ---

1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is

--- Content provided by FirstRanker.com ---

>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;

--- Content provided by FirstRanker.com ---

>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands

--- Content provided by FirstRanker.com ---

and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 9

--- Content provided by FirstRanker.com ---

1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];

--- Content provided by FirstRanker.com ---

>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A

--- Content provided by FirstRanker.com ---

Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];

--- Content provided by FirstRanker.com ---

(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;

--- Content provided by FirstRanker.com ---

Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:

--- Content provided by FirstRanker.com ---

>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];

--- Content provided by FirstRanker.com ---

>>B= [6 5; 3 1];
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

--- Content provided by FirstRanker.com ---

?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

--- Content provided by FirstRanker.com ---

EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

Name :
Register No. :
Class :

LABORATORY MANUAL

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

--- Content provided by FirstRanker.com ---

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

--- Content provided by FirstRanker.com ---

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

--- Content provided by FirstRanker.com ---

ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

--- Content provided by FirstRanker.com ---

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

--- Content provided by FirstRanker.com ---

education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

--- Content provided by FirstRanker.com ---

To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

--- Content provided by FirstRanker.com ---

broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

--- Content provided by FirstRanker.com ---

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

--- Content provided by FirstRanker.com ---

c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

--- Content provided by FirstRanker.com ---

g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

--- Content provided by FirstRanker.com ---

k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES

--- Content provided by FirstRanker.com ---

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

--- Content provided by FirstRanker.com ---

1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

--- Content provided by FirstRanker.com ---

6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

--- Content provided by FirstRanker.com ---

1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

--- Content provided by FirstRanker.com ---

4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

--- Content provided by FirstRanker.com ---

analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

--- Content provided by FirstRanker.com ---

siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

--- Content provided by FirstRanker.com ---

machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY

--- Content provided by FirstRanker.com ---

CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

--- Content provided by FirstRanker.com ---

3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

--- Content provided by FirstRanker.com ---

CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

--- Content provided by FirstRanker.com ---

12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

--- Content provided by FirstRanker.com ---

Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

--- Content provided by FirstRanker.com ---

Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

--- Content provided by FirstRanker.com ---

tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

--- Content provided by FirstRanker.com ---

? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

--- Content provided by FirstRanker.com ---

MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

--- Content provided by FirstRanker.com ---

1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 7

To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

--- Content provided by FirstRanker.com ---

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

--- Content provided by FirstRanker.com ---

i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

--- Content provided by FirstRanker.com ---

M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

--- Content provided by FirstRanker.com ---

series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

--- Content provided by FirstRanker.com ---

methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

--- Content provided by FirstRanker.com ---

has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 8

4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

--- Content provided by FirstRanker.com ---

helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

--- Content provided by FirstRanker.com ---

commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

--- Content provided by FirstRanker.com ---

positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

--- Content provided by FirstRanker.com ---

command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

--- Content provided by FirstRanker.com ---

>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

--- Content provided by FirstRanker.com ---

in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 9

--- Content provided by FirstRanker.com ---

1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

--- Content provided by FirstRanker.com ---

>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

--- Content provided by FirstRanker.com ---

>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

--- Content provided by FirstRanker.com ---

>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

--- Content provided by FirstRanker.com ---

>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

--- Content provided by FirstRanker.com ---

Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

--- Content provided by FirstRanker.com ---

>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 10

>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

--- Content provided by FirstRanker.com ---

]Looping :

--- Content provided by FirstRanker.com ---

>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

--- Content provided by FirstRanker.com ---

VII SEMESTER - R 2013

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

Name :

--- Content provided by FirstRanker.com ---

Register No. :
Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

--- Content provided by FirstRanker.com ---

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and

--- Content provided by FirstRanker.com ---

soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING

--- Content provided by FirstRanker.com ---

To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

--- Content provided by FirstRanker.com ---

? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and

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ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

--- Content provided by FirstRanker.com ---

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education

--- Content provided by FirstRanker.com ---

2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables

--- Content provided by FirstRanker.com ---

them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context

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5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)

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a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical

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and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large

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h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY

--- Content provided by FirstRanker.com ---

SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines

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2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System

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7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

--- Content provided by FirstRanker.com ---

1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance

--- Content provided by FirstRanker.com ---

matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.

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8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.

--- Content provided by FirstRanker.com ---

11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.

--- Content provided by FirstRanker.com ---

14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS

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Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19

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4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS

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8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58

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Mini Project
13 Modeling of FACTS devices using SIMULINK 68
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

Expt. No.1: INTRODUCTION TO MATLAB

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Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:

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1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and

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communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development

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? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical

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manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:

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To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.

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Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file

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M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined

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function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.

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>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic

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equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.

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>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common

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data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.

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1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is

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>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;

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>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands

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and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 9

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];

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>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A

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Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];

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(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;

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Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:

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>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];

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>>B= [6 5; 3 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 10

>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.

--- Content provided by FirstRanker.com ---

>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,

--- Content provided by FirstRanker.com ---

element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.

--- Content provided by FirstRanker.com ---

To explore these simply type
>>help if
>>help for
>>help while
Example :

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end

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- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 11

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);

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To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)

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>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.

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1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s

--- Content provided by FirstRanker.com ---

usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;

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1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.

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To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

--- Content provided by FirstRanker.com ---

?

--- Content provided by FirstRanker.com ---

DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

--- Content provided by FirstRanker.com ---

EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

--- Content provided by FirstRanker.com ---

Name :
Register No. :
Class :

--- Content provided by FirstRanker.com ---

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

--- Content provided by FirstRanker.com ---

is committed to provide highly disciplined, conscientious and

--- Content provided by FirstRanker.com ---

enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

--- Content provided by FirstRanker.com ---

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

--- Content provided by FirstRanker.com ---

DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

--- Content provided by FirstRanker.com ---

? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

--- Content provided by FirstRanker.com ---

communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

--- Content provided by FirstRanker.com ---

enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

--- Content provided by FirstRanker.com ---

3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

--- Content provided by FirstRanker.com ---

students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

--- Content provided by FirstRanker.com ---

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

--- Content provided by FirstRanker.com ---

such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

--- Content provided by FirstRanker.com ---

f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

--- Content provided by FirstRanker.com ---

j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES

--- Content provided by FirstRanker.com ---

COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

--- Content provided by FirstRanker.com ---

LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

--- Content provided by FirstRanker.com ---

5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

--- Content provided by FirstRanker.com ---

10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

--- Content provided by FirstRanker.com ---

3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

--- Content provided by FirstRanker.com ---

7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

--- Content provided by FirstRanker.com ---

10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

--- Content provided by FirstRanker.com ---

13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

--- Content provided by FirstRanker.com ---

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

--- Content provided by FirstRanker.com ---

2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

--- Content provided by FirstRanker.com ---

MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 10

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

LABORATORY MANUAL

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

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ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

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3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

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CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

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12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

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Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

--- Content provided by FirstRanker.com ---

tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

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? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

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MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

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1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 7

To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

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M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

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series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

--- Content provided by FirstRanker.com ---

methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

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has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 8

4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

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helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

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commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

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positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

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command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

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>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

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in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 9

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

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>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

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>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

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>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

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>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

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Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

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>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 10

>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;

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>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);

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>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a

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pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some

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input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?

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z= [5 2 4;
1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;

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1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;

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1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2

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Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.

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Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics

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Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming

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in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations

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4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?

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Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i

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8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.

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10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?

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Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?

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Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce

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FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :

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Register No. :
Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and

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soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING

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To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and

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ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education

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2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables

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them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context

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5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)

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a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical

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and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large

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h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines

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2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System

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7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance

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matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.

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8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.

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11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.

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14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS

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Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19

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4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS

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8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58

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Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB

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Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:

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1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and

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communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development

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? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical

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manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:

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To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.

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Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file

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M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined

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function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.

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>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic

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equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.

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>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common

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data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.

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1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is

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>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;

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>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands

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and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];

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>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A

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Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];

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(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;

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Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:

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>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];

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>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.

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>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,

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element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.

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To explore these simply type
>>help if
>>help for
>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end

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- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 11

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);

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To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)

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>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.

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1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s

--- Content provided by FirstRanker.com ---

usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;

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1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.

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To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)

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y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]

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>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available

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in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:

--- Content provided by FirstRanker.com ---

Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

--- Content provided by FirstRanker.com ---

Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping

--- Content provided by FirstRanker.com ---

Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

--- Content provided by FirstRanker.com ---

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

--- Content provided by FirstRanker.com ---

2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?

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For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi

--- Content provided by FirstRanker.com ---

domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?

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poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?

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Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,

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12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application

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development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:

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Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of

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D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have

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a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

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communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13


1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 15

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

LABORATORY MANUAL

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

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ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
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COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

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3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

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CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

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12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

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Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

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tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

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? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

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MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

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1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

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M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

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series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

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methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

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has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

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helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

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commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

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positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

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command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

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>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

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in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

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>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

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>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

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>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

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>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

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Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

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>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;

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>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);

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>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a

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pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some

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input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?

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z= [5 2 4;
1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;

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1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;

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1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2

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Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.

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Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics

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Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming

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in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations

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4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?

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Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i

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8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.

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10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?

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Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?

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Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and

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double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1

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A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');

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d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))

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fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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FirstRanker.com - FirstRanker's Choice
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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :

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Register No. :
Class :

LABORATORY MANUAL
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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and

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soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING

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To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and

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ethical practices
MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education

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2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables

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them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context

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5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)

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a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical

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and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large

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h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines

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2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System

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7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance

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matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.

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8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.

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11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.

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14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS

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Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19

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4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS

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8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58

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Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB

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Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:

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1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and

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communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development

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? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical

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manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:

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To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.

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Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file

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M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined

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function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.

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>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic

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equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.

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>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common

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data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.

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1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is

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>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;

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>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands

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and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];

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>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A

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Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];

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(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;

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Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:

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>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];

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>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.

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>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,

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element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.

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To explore these simply type
>>help if
>>help for
>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end

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- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);

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To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)

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>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.

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1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s

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usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;

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1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.

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To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)

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y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]

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>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available

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in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:

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Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping

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Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

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2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?

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For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi

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domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?

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poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?

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Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,

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12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application

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development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce
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Aim:

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Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of

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D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have

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a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:

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%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');

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r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);

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fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2

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A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various

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cases.
Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');

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H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);

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a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;

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c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);

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Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);

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DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
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VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

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communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y

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capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase

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per Kilometer of the line.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit

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%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;

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Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;

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a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);

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Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);

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Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);

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DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)

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L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving

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parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

LABORATORY MANUAL

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

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ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

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3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

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CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

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12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

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Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

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tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

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? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

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MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

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1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

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M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

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series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

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methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

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has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

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helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

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commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

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positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

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command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

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>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

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in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

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>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

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>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

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>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

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>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

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Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

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>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 11

Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;

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>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);

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>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a

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pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some

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input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?

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z= [5 2 4;
1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;

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1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;

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1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2

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Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.

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Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics

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Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13


1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming

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in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations

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4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?

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Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i

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8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.

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10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?

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Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?

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Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and

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double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1

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A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 15

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');

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d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))

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fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit
%3 phase double circuit

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S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');

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S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;

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b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);

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Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);

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Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);

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DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km

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C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:

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Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.

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2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines

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also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling

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5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically

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used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.

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8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?

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When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission

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line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :

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Register No. :
Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and

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soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING

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To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and

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ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education

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2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables

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them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context

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5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)

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a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical

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and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large

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h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines

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2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System

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7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance

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matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.

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8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.

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11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.

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14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS

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Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19

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4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS

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8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58

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Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB

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Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:

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1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and

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communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development

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? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical

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manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:

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To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.

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Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file

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M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined

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function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.

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>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic

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equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.

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>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common

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data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.

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1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is

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>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;

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>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands

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and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];

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>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A

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Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];

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(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;

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Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:

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>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];

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>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.

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>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,

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element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.

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To explore these simply type
>>help if
>>help for
>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end

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- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);

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To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)

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>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.

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1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s

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usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;

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1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.

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To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)

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y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]

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>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available

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in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:

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Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping

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Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

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2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?

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For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi

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domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?

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poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?

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Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,

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12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application

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development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:

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Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of

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D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have

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a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:

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%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');

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r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);

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fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2

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A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various

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cases.
Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');

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H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);

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a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;

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c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);

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Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);

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DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;

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GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);

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DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km

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Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double

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circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?

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GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.

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4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?

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A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight

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and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?

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9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-

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section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load

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is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE

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PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).

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Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:

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Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application

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It is used in transmission and distribution of electrical power system.
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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

LABORATORY MANUAL

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

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ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
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COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

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3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

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CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

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12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

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Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

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tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

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? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

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MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

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1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

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M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

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series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

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methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

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has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

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helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

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commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

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positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

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command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

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>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

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in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

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>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

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>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

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>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

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>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

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Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

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>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;

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>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);

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>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a

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pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some

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input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?

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z= [5 2 4;
1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;

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1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;

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1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2

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Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.

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Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics

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Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming

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in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations

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4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?

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Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i

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8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.

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10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?

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Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?

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Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and

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double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1

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A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');

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d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))

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fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit
%3 phase double circuit

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S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');

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S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;

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b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);

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Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);

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Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);

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DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km

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C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:

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Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.

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2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines

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also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling

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5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically

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used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.

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8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?

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When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission

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line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.

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Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.

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Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load

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2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.

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4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?

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1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.

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Viva - voce
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

LABORATORY MANUAL

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

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ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

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3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

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CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

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12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

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Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

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tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

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? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

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MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

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1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

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M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

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series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

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methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

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has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

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helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

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commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

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positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

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command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

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>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

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in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

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>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

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>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

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>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

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>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

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Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

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>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;

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>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);

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>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a

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pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some

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input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?

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z= [5 2 4;
1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;

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1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;

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1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2

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Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.

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Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics

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Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13


1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming

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in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations

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4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?

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Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i

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8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.

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10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?

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Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?

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Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and

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double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1

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A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');

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d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))

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fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit
%3 phase double circuit

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S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');

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S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;

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b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);

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Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);

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Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);

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DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km

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C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:

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Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.

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2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines

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also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling

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5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically

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used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.

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8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?

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When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission

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line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.

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Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.

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Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load

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2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.

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4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?

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1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6

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Theory:
Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every

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transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus

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matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance

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matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:

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Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)

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Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION

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VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

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deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

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? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

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MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals

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To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and

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training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism

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To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,

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through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field

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b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems

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e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility

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i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.

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4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems

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9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.

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2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.

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6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi

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machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.

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12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS

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1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26

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6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41

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10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68

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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems

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Software required:
MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and

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programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.

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1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization

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? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small

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and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit

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(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,

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where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing

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them.
M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be

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called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace

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>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more

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generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the

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Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators

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2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)

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Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?

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>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in

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the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the

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workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence

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of commands
>>a=2;
>>b=5;
>>whos
>>clear all

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The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any

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DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is

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concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are

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considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,

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whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B

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Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)

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1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;

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>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];

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>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just

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>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if

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>>help for
>>help while
Example :

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]Looping :


>>if z=0
>>y=0

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>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:

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MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.

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>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)

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To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);

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The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The

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commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function

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We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.

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function y = admin(z)
y = 1./z
return

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Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,

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ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation

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Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:
MATLAB Used

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Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation

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Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield

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3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?

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If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.

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7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?

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An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application

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Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD

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GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 15

(b) Verify the results using the MATLAB program.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');

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D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;

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x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);

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inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of

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1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:

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%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');

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dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;

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c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);

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Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);

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Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;

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Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)

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GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19



1. What is meant by geometric mean distance?

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GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?

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transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The

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high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.

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6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.

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Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such

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as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.

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11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor

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Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
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Algorithm:

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Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.

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Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit

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3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?

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The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network

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Software required:
MATLAB 7.6
Theory:
Formation of Y
bus

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matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.

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Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful

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in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing

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buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:

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Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:

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(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
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VISION

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VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

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deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

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? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

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MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals

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To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and

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training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism

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To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,

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through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field

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b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems

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e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility

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i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.

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4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems

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9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.

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2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.

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6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi

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machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.

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12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS

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1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26

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6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41

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10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68

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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems

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Software required:
MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and

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programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.

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1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization

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? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small

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and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit

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(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,

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where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing

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them.
M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be

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called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace

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>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more

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generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the

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Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators

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2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)

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Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?

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>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in

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the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the

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workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence

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of commands
>>a=2;
>>b=5;
>>whos
>>clear all

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The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any

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DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is

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concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are

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considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,

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whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B

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Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)

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1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;

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>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];

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>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just

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>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if

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>>help for
>>help while
Example :

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]Looping :


>>if z=0
>>y=0

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>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:

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MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.

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>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)

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To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);

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The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The

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commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function

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We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.

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function y = admin(z)
y = 1./z
return

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Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,

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ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation

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Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:
MATLAB Used

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Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation

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Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield

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3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?

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If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.

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7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?

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An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application

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Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD

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GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');

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D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;

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x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);

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inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of

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1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:

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%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');

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dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;

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c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);

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Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);

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Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;

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Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)

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GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19



1. What is meant by geometric mean distance?

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GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?

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transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The

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high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.

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6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.

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Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such

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as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.

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11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor

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Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:

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Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.

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Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit

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3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?

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The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network

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Software required:
MATLAB 7.6
Theory:
Formation of Y
bus

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matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.

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Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful

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in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing

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buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:

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Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:

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(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03

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2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01

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4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....

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clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...

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tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...

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y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...

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FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :

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Register No. :
Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and

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soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING

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To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and

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ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education

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2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables

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them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context

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5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)

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a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical

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and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large

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h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines

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2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System

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7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance

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matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.

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8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.

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11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.

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14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS

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Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19

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4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS

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8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58

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Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB

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Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:

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1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and

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communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development

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? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical

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manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:

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To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.

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Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file

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M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined

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function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.

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>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic

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equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.

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>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common

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data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.

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1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is

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>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;

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>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands

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and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];

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>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A

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Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];

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(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;

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Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:

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>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];

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>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.

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>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,

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element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.

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To explore these simply type
>>help if
>>help for
>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end

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- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);

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To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)

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>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.

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1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s

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usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;

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1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.

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To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)

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y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]

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>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available

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in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:

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Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping

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Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

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2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?

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For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi

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domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?

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poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?

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Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,

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12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application

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development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce
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Aim:

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Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of

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D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have

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a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:

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%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');

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r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);

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fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2

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A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various

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cases.
Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');

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H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);

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a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;

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c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);

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Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);

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DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;

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GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);

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DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km

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Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double

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circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?

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GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.

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4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?

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A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight

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and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?

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9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-

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section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load

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is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE

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PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).

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Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:

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Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application

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It is used in transmission and distribution of electrical power system.
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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?

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Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?

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The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?

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2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:

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Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element

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corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:

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In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can

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be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.

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Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)

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Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
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Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.

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5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.

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Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02

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1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025

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3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')

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linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...

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b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...

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nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
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% Formation of the Off Diagonal Elements...

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for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....

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for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end

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end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus

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Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus

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admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study

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FirstRanker.com - FirstRanker's Choice
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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :

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Register No. :
Class :

LABORATORY MANUAL
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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and

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soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING

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To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and

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ethical practices
MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education

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2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables

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them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context

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5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)

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a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical

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and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large

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h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines

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2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System

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7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance

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matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.

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8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.

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11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.

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14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS

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Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19

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4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS

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8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58

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Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB

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Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:

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1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and

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communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development

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? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical

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manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:

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To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.

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Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file

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M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined

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function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.

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>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic

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equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.

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>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common

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data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.

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1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is

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>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;

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>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands

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and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];

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>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A

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Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];

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(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;

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Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:

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>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];

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>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.

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>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,

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element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.

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To explore these simply type
>>help if
>>help for
>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end

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- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);

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To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)

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>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.

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1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s

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usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;

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1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.

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To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)

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y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]

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>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available

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in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:

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Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping

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Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

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2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?

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For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi

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domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?

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poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?

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Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,

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12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application

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development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:

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Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of

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D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have

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a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:

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%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');

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r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 16

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);

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fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2

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A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various

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cases.
Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');

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H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);

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a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;

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c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);

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Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);

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DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;

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GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);

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DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km

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Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double

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circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?

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GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.

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4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?

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A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight

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and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?

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9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-

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section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load

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is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE

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PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).

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Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:

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Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?

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Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?

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The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?

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2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:

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Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element

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corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:

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In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can

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be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.

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Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)

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Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.

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5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02

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1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025

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3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')

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linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...

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b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...

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nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...

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for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....

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for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end

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end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus

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Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus

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admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27


1. What is meant by singular transformation method?
The matrix formed by graph theory.

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2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?

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Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.

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7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?

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Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.

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Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

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communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13


1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 15

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y

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capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase

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per Kilometer of the line.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit

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%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;

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Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;

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a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);

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Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);

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Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);

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DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)

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L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving

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parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture

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when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next

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physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.

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This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?

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Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several

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advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.

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10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?

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In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:

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To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.

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Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium

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transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?

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Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?

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Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.

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6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND

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IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:

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MATLAB 7.6
Theory:
Formation of Y
bus
matrix:

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Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z

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bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.

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The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.

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Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)

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Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.

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(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
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Line data:

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From To R X B/2

Bus Bus

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1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01

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2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04

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5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....
clc

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fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...

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r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...

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b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));

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end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m

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ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end
ybus = ybus % Bus Admittance Matrix

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zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:

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Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?

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Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view

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6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?

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Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm

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2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power

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system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.

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3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:

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Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.

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FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :

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Register No. :
Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and

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soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING

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To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and

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ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education

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2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables

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them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context

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5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)

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a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical

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and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large

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h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines

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2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System

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7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance

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matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.

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8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.

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11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.

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14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS

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Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19

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4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS

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8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58

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Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB

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Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:

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1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and

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communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development

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? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical

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manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:

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To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.

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Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file

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M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined

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function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.

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>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic

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equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.

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>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common

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data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.

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1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is

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>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;

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>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands

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and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];

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>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A

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Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];

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(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;

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Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:

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>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];

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>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.

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>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,

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element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.

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To explore these simply type
>>help if
>>help for
>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end

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- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);

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To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)

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>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.

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1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s

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usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;

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1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.

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To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)

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y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]

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>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available

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in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:

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Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping

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Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

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2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?

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For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi

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domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?

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poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?

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Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,

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12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application

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development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:

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Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of

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D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have

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a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:

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%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');

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r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);

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fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2

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A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various

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cases.
Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');

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H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);

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a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;

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c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);

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Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);

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DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;

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GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);

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DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km

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Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double

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circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?

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GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.

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4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?

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A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight

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and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?

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9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-

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section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load

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is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE

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PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).

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Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:

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Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?

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Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?

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The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?

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2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:

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Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element

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corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:

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In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can

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be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.

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Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)

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Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.

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5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02

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1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025

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3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')

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linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...

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b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...

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nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
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% Formation of the Off Diagonal Elements...

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for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....

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for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end

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end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus

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Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus

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admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study

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1. What is meant by singular transformation method?
The matrix formed by graph theory.

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2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?

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Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.

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7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?

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Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.

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Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA

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POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:

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MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power

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supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.

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5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit

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The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
FirstRanker.com - FirstRanker's Choice

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?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 16

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
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Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
FirstRanker.com - FirstRanker's Choice
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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
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VISION

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VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

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deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

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? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

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MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals

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To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and

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training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism

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To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,

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through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field

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b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems

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e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility

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i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.

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4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems

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9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.

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2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.

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6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi

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machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.

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12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS

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1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26

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6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41

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10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68

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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems

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Software required:
MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and

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programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.

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1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization

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? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small

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and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit

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(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,

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where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing

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them.
M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be

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called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace

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>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more

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generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the

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Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators

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2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)

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Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?

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>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in

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the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the

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workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence

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of commands
>>a=2;
>>b=5;
>>whos
>>clear all

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The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any

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DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is

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concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are

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considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,

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whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B

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Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)

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1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;

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>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];

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>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just

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>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if

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>>help for
>>help while
Example :

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]Looping :


>>if z=0
>>y=0

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>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:

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MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.

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>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)

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To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);

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The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The

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commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function

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We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.

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function y = admin(z)
y = 1./z
return

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Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,

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ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation

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Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:
MATLAB Used

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Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation

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Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield

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3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?

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If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.

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7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?

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An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application

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Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD

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GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');

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D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;

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x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);

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inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of

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1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
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Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:

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%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');

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dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;

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c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);

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Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);

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Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;

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Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)

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GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19



1. What is meant by geometric mean distance?

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GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?

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transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The

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high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.

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6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.

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Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such

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as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.

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11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor

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Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:

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Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.

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Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit

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3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?

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The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network

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Software required:
MATLAB 7.6
Theory:
Formation of Y
bus

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matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.

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Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful

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in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing

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buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:

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Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:

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(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03

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2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01

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4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....

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clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...

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tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...

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y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);

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ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch

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if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end

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ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using

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MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.

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3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?

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Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method

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8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?

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1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates

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the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:

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1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.

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(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce

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Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant

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3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.

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5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?

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Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

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communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13


1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 15

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y

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capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase

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per Kilometer of the line.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit

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%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;

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Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;

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a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);

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Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);

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Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);

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DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)

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L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving

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parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture

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when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next

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physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.

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This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?

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Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several

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advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.

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10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?

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In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:

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To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.

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Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium

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transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?

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Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?

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Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.

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6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND

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IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:

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MATLAB 7.6
Theory:
Formation of Y
bus
matrix:

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Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z

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bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.

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The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.

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Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)

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Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.

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(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus

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1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01

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2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04

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5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....
clc

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fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...

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r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...

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b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));

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end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m

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ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end
ybus = ybus % Bus Admittance Matrix

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zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:

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Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?

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Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view

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6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?

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Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm

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2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power

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system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.

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3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:

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Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady

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state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink

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Application:
To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?

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If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?

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In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?

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Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop

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Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power

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system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model

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3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9

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Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is

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computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

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communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13


1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 15

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y

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capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase

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per Kilometer of the line.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit

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%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;

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Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;

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a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);

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Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);

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Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);

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DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)

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L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving

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parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture

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when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next

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physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.

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This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?

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Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several

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advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.

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10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?

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In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:

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To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.

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Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium

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transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?

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Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?

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Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.

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6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND

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IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:

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MATLAB 7.6
Theory:
Formation of Y
bus
matrix:

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Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z

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bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.

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The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.

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Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)

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Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.

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(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
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Line data:

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From To R X B/2

Bus Bus

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1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01

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2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04

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5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....
clc

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fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...

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r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...

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b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));

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end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m

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ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end
ybus = ybus % Bus Admittance Matrix

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zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:

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Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?

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Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view

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6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?

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Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm

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2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power

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system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.

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3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:

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Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady

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state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink

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Application:
To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?

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If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?

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In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?

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Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop

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Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power

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system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model

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3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9

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Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is

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computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the

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frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop

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Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce

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FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :

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Register No. :
Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and

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soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING

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To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and

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ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education

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2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables

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them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context

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5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)

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a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical

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and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large

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h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines

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2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System

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7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance

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matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.

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8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.

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11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.

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14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS

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Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19

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4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS

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8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58

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Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB

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Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:

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1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and

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communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development

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? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical

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manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:

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To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.

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Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file

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M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined

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function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.

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>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic

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equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.

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>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common

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data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.

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1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is

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>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;

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>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands

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and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];

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>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A

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Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];

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(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;

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Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:

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>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];

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>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.

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>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,

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element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.

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To explore these simply type
>>help if
>>help for
>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end

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- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);

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To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)

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>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.

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1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s

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usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;

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1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.

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To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)

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y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]

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>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available

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in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:

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Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping

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Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

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2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?

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For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi

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domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?

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poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?

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Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,

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12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application

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development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:

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Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of

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D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have

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a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:

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%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');

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r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);

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fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2

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A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various

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cases.
Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');

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H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);

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a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;

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c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);

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Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);

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DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;

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GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);

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DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km

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Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double

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circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?

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GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.

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4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?

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A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight

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and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?

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9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-

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section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load

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is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE

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PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).

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Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:

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Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?

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Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?

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The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?

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2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:

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Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element

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corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:

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In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can

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be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.

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Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)

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Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.

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5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02

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1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025

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3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')

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linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...

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b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...

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nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
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% Formation of the Off Diagonal Elements...

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for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....

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for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end

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end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus

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Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus

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admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study

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1. What is meant by singular transformation method?
The matrix formed by graph theory.

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2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?

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Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.

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7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?

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Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.

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Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA

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POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:

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MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power

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supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.

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5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit

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The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2

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sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?

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Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load

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4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?

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frequency control channel.
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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM

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Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:

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MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.

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A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram

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5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
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Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA

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Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.

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(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and

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without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34


Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet

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the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?

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a and b
4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

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Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:

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To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:

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Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may

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come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small

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disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run

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5. View the results
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

LABORATORY MANUAL

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

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ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

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3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

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CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

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12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

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Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

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tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

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? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

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MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

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1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

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M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

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series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

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methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

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has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

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helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

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commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

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positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

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command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

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>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

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in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

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>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

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>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

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>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

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>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

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Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

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>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;

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>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);

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>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a

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pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some

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input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?

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z= [5 2 4;
1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;

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1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;

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1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2

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Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.

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Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics

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Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming

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in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations

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4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?

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Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i

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8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.

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10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?

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Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?

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Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and

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double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1

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A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');

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d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))

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fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit
%3 phase double circuit

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S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');

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S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;

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b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);

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Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);

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Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);

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DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km

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C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:

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Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.

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2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines

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also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling

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5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically

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used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.

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8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?

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When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission

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line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.

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Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.

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Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load

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2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.

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4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?

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1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6

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Theory:
Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every

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transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus

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matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance

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matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:

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Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)

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Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.

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(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02

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1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02

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2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')

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fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...

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x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...

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nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end

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% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);

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end
end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix

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zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis

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Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27


1. What is meant by singular transformation method?

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The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.

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4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?

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loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance

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9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus

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11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.

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4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec

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Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with

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and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:

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To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple

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generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop

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7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the

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AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA

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POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram

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4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

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Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4

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Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in

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area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34


Application:

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To maintain the power and frequency constant in electrical power system.



1. What is meant by two area system?

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power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant

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3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop
Current control loop

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5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

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Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.

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(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:

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A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =

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0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.

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Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION

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VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

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deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

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? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

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MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals

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To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and

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training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism

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To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,

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through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field

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b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems

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e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility

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i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.

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4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems

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9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.

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2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.

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6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi

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machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.

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12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS

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1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26

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6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41

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10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems

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Software required:
MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and

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programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.

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1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization

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? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small

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and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit

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(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,

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where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing

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them.
M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be

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called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace

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>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more

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generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the

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Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators

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2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)

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Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?

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>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in

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the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the

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workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence

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of commands
>>a=2;
>>b=5;
>>whos
>>clear all

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The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any

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DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is

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concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are

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considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,

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whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B

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Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)

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1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;

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>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];

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>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just

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>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if

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>>help for
>>help while
Example :

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]Looping :


>>if z=0
>>y=0

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>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:

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MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.

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>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)

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To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);

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The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The

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commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function

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We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.

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function y = admin(z)
y = 1./z
return

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Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,

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ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation

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Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:
MATLAB Used

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Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation

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Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield

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3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?

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If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.

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7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?

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An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application

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Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD

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GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');

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D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;

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x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);

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inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of

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1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:

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%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');

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dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;

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c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);

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Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);

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Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;

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Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)

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GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19



1. What is meant by geometric mean distance?

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GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?

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transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The

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high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.

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6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.

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Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such

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as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.

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11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor

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Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:

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Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.

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Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit

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3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?

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The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network

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Software required:
MATLAB 7.6
Theory:
Formation of Y
bus

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matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.

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Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful

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in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing

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buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:

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Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:

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(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03

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2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01

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4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....

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clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...

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tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...

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y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);

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ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch

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if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end

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ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using

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MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.

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3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?

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Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method

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8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?

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1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates

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the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:

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1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.

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(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce

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Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant

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3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.

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5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?

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Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the

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governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:

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A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625

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damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec

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The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).

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Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?

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Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?

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Frequency control loop
Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS

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SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=

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0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both

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lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program


Result:

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Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37



1. What is meant by stability?

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Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively

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large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network

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4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.

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6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of

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synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.

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A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
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Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
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% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2

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Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec

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Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.

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(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b

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4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY

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ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-

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Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1

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=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were

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analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?

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The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a

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power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging

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with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle

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The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?

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9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:

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To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6
Theory:

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Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1

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(k)
, PG 2
(k)
, ?PG N
(K)

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}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:

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Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.

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4. Execute the program by either pressing Tools ? Run.
5. View the results.
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

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communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y

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capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase

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per Kilometer of the line.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit

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%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;

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Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;

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a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);

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Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);

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Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);

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DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)

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L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving

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parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture

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when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next

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physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.

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This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?

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Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several

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advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.

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10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?

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In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:

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To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.

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Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium

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transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?

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Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?

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Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.

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6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND

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IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:

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MATLAB 7.6
Theory:
Formation of Y
bus
matrix:

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Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z

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bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.

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The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.

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Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)

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Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.

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(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus

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1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01

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2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04

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5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....
clc

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fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...

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r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...

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b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));

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end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m

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ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end
ybus = ybus % Bus Admittance Matrix

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zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:

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Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?

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Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view

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6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?

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Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm

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2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power

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system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.

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3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:

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Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady

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state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink

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Application:
To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?

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If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?

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In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?

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Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop

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Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power

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system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model

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3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9

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Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is

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computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the

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frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop

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Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:

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MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are

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marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.

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b) Verify the result using MATLAB program


Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)

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system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of

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operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.

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is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time

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The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time

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The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism

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8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.

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Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses

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Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:

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In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2

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(k)
, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which

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minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma

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Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1

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2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW

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C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.

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Program:
clc;
clear all;
warning off;
a=[.004; .006; .009];

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b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');

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fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;

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p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])

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lambda=lambda+dellambda;
end
lambda
p
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 16

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
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Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2

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Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec

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Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.

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(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b

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4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY

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ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-

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Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1

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=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were

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analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?

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The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a

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power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging

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with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle

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The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?

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9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:

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To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6
Theory:

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Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1

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(k)
, PG 2
(k)
, ?PG N
(K)

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}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:

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Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.

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4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;

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warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;

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delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;

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while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));

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dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda

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p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:

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Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =

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8.5000
p =
400.0000
250.0000
150.0000

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Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2

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; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW

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100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc

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n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 9

1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 10

>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
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Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
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% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2

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Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec

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Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.

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(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b

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4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY

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ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-

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Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1

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=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were

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analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?

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The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a

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power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging

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with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle

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The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?

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9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:

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To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6
Theory:

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Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1

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(k)
, PG 2
(k)
, ?PG N
(K)

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}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:

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Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.

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4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;

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warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;

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delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;

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while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));

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dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda

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p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:

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Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =

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8.5000
p =
400.0000
250.0000
150.0000

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Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2

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; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW

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100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc

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n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;

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for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;

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for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg

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for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))

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Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end
end

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Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)

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x1=0;
y1=0;
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

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communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y

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capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase

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per Kilometer of the line.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit

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%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;

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Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;

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a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);

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Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);

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Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);

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DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)

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L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving

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parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture

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when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next

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physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.

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This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?

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Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several

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advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.

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10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?

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In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:

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To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.

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Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium

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transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?

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Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?

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Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.

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6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND

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IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:

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MATLAB 7.6
Theory:
Formation of Y
bus
matrix:

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Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z

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bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.

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The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.

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Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)

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Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.

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(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus

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1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01

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2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04

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5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....
clc

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fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...

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r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...

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b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));

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end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m

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ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end
ybus = ybus % Bus Admittance Matrix

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zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:

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Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?

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Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view

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6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?

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Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm

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2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power

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system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.

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3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:

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Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady

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state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink

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Application:
To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?

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If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?

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In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?

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Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop

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Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power

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system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model

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3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9

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Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is

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computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the

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frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop

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Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:

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MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are

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marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.

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b) Verify the result using MATLAB program


Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)

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system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of

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operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.

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is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time

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The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time

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The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism

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8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.

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Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses

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Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:

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In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2

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(k)
, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which

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minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma

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Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1

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2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW

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C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.

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Program:
clc;
clear all;
warning off;
a=[.004; .006; .009];

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b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');

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fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;

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p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])

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lambda=lambda+dellambda;
end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda

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10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =

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400.0000
250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.

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Program:
clear
clc
n=3;
demand=925;

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a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
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c=[640 580 820];

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Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));

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y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));

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Pgtotal=sum(Pg);
end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));

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Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else

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Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);
end

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Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;

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for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));

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end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end

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end
end
Pg
Output:
lambda =

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8.6149
Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598

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Demand new =
575
Lambda new =
8.7147
Pg =

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350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:

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By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION

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VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

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deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

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? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

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MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals

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To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and

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training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism

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To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,

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through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field

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b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems

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e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility

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i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.

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4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems

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9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.

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2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.

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6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi

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machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.

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12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS

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1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26

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6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41

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10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68

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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems

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Software required:
MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and

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programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.

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1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization

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? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small

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and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit

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(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,

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where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing

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them.
M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be

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called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace

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>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more

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generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the

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Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators

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2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)

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Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?

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>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in

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the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the

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workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence

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of commands
>>a=2;
>>b=5;
>>whos
>>clear all

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The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any

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DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is

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concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are

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considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,

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whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B

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Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)

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1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;

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>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];

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>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just

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>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if

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>>help for
>>help while
Example :

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]Looping :


>>if z=0
>>y=0

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>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:

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MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.

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>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)

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To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);

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The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The

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commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function

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We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.

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function y = admin(z)
y = 1./z
return

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Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,

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ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation

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Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:
MATLAB Used

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Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation

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Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield

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3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?

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If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.

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7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?

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An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application

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Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD

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GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');

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D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;

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x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);

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inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of

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1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:

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%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');

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dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;

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c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);

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Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);

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Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;

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Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)

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GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19



1. What is meant by geometric mean distance?

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GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?

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transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The

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high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.

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6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.

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Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such

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as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.

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11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor

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Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:

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Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.

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Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit

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3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?

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The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network

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Software required:
MATLAB 7.6
Theory:
Formation of Y
bus

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matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.

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Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful

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in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing

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buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:

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Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:

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(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03

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2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01

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4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....

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clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...

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tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...

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y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);

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ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch

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if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end

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ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using

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MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.

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3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?

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Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method

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8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?

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1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates

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the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:

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1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.

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(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce

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Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant

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3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.

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5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?

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Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the

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governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:

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A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625

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damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec

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The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).

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Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?

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Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?

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Frequency control loop
Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS

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SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=

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0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both

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lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program


Result:

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Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37



1. What is meant by stability?

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Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively

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large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network

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4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.

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6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of

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synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.

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A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and

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without line losses
Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:

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Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)

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, PG 2
(k)
, ?PG N
(K)
}; k = 1,2,? .... N S

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Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program

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Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.

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5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;

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P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost

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in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;
warning off;

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a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;

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lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001

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iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;

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disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda
p

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10

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lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000

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p =
400.0000
250.0000
150.0000
Total cost = 6.6825e+003

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Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW

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C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2

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; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW

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Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc
n=3;

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demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n

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x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n

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Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg
for i=1:n

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if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);

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else
Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);

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end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;

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y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n
x1=x1+(b(i)/(2*a(i)));

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y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));

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end
end
end
Pg
Output:

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lambda =
8.6149
Pg =
367.4040 379.4361 178.1598
Pg =

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350.0000 379.4361 178.1598
Demand new =
575
Lambda new =
8.7147

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Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.

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Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch

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Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment

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Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.

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Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?

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Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION

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VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

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deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

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? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

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MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals

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To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and

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training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism

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To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,

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through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field

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b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems

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e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility

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i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.

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4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems

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9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.

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2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.

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6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi

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machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.

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12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS

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1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26

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6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41

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10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems

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Software required:
MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and

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programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.

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1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization

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? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small

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and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit

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(Or)
>>exit
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 7

To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,

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where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing

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them.
M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be

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called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace

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>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more

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generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the

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Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators

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2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)

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Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?

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>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in

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the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the

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workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence

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of commands
>>a=2;
>>b=5;
>>whos
>>clear all

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The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any

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DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is

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concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are

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considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,

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whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B

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Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)

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1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;

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>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];

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>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just

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>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if

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>>help for
>>help while
Example :

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]Looping :


>>if z=0
>>y=0

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>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:

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MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.

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>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)

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To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);

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The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The

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commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function

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We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.

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function y = admin(z)
y = 1./z
return

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Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,

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ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation

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Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:
MATLAB Used

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Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation

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Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield

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3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?

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If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.

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7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?

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An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application

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Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD

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GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');

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D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;

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x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);

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inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of

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1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:

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%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');

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dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;

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c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);

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Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);

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Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;

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Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)

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GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19



1. What is meant by geometric mean distance?

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GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?

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transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The

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high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.

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6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.

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Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such

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as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.

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11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor

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Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:

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Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.

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Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit

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3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?

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The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network

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Software required:
MATLAB 7.6
Theory:
Formation of Y
bus

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matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.

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Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful

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in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing

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buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:

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Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:

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(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03

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2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01

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4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....

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clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...

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tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...

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y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);

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ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch

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if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end

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ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using

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MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.

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3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?

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Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method

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8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?

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1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates

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the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:

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1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.

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(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce

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Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant

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3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.

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5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?

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Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the

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governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:

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A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625

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damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec

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The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).

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Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?

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Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?

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Frequency control loop
Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS

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SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=

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0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both

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lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program


Result:

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Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37



1. What is meant by stability?

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Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively

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large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network

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4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.

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6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of

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synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.

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A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and

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without line losses
Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:

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Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)

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, PG 2
(k)
, ?PG N
(K)
}; k = 1,2,? .... N S

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Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program

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Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.

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5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;

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P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost

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in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;
warning off;

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a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;

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lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001

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iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;

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disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda
p

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10

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lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000

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p =
400.0000
250.0000
150.0000
Total cost = 6.6825e+003

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Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW

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C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2

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; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW

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Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc
n=3;

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demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n

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x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n

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Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg
for i=1:n

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if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);

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else
Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);

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end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;

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y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n
x1=x1+(b(i)/(2*a(i)));

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y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));

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end
end
end
Pg
Output:

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lambda =
8.6149
Pg =
367.4040 379.4361 178.1598
Pg =

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350.0000 379.4361 178.1598
Demand new =
575
Lambda new =
8.7147

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Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.

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Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch

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Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment

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Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.

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Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?

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Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI

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MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:

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MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
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VISION

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VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

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deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

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? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

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MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals

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To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and

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training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism

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To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,

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through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field

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b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems

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e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility

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i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.

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4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems

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9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.

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2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.

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6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi

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machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.

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12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS

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1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26

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6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41

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10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68

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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems

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Software required:
MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and

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programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.

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1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization

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? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small

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and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit

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(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,

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where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing

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them.
M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be

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called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace

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>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more

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generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the

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Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators

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2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)

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Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?

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>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in

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the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the

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workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence

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of commands
>>a=2;
>>b=5;
>>whos
>>clear all

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The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any

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DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is

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concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are

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considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,

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whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B

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Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)

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1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;

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>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];

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>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just

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>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if

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>>help for
>>help while
Example :

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]Looping :


>>if z=0
>>y=0

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>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:

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MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.

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>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)

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To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);

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The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The

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commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function

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We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.

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function y = admin(z)
y = 1./z
return

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Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,

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ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation

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Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:
MATLAB Used

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Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation

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Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield

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3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?

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If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.

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7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?

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An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application

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Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD

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GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');

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D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;

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x=D12*D23*D31;
Deq=nthroot(x,3);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 16

Y=log(Deq/Ds);

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inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of

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1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:

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%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');

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dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;

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c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);

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Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);

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Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;

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Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)

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GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19



1. What is meant by geometric mean distance?

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GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?

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transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The

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high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.

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6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.

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Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such

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as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.

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11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor

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Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:

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Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.

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Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit

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3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?

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The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network

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Software required:
MATLAB 7.6
Theory:
Formation of Y
bus

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matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.

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Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful

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in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing

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buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:

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Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:

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(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03

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2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01

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4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....

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clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...

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tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...

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y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);

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ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch

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if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end

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ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using

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MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.

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3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?

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Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method

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8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?

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1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates

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the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:

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1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.

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(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce

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Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant

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3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.

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5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?

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Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the

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governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:

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A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625

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damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec

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The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).

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Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?

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Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?

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Frequency control loop
Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS

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SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=

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0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both

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lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program


Result:

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Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37



1. What is meant by stability?

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Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively

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large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network

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4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.

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6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of

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synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.

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A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and

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without line losses
Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:

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Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)

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, PG 2
(k)
, ?PG N
(K)
}; k = 1,2,? .... N S

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Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program

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Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.

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5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;

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P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost

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in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;
warning off;

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a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;

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lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001

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iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;

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disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda
p

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10

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lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000

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p =
400.0000
250.0000
150.0000
Total cost = 6.6825e+003

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Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW

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C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2

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; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW

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Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc
n=3;

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demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n

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x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n

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Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg
for i=1:n

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if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);

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else
Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);

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end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;

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y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n
x1=x1+(b(i)/(2*a(i)));

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y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));

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end
end
end
Pg
Output:

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lambda =
8.6149
Pg =
367.4040 379.4361 178.1598
Pg =

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350.0000 379.4361 178.1598
Demand new =
575
Lambda new =
8.7147

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Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.

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Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch

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Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment

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Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.

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Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?

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Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI

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MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:

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MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.

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(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1

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- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:

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For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)

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Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION

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VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

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deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

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? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

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MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals

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To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and

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training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism

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To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,

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through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field

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b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems

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e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility

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i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.

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4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems

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9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.

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2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.

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6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi

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machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.

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12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS

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1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26

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6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41

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10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems

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Software required:
MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and

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programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.

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1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization

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? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small

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and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit

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(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,

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where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing

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them.
M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be

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called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace

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>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more

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generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the

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Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators

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2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)

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Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?

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>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in

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the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the

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workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence

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of commands
>>a=2;
>>b=5;
>>whos
>>clear all

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The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any

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DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is

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concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are

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considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,

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whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B

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Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)

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1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;

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>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];

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>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just

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>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if

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>>help for
>>help while
Example :

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]Looping :


>>if z=0
>>y=0

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>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:

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MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.

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>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)

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To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);

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The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The

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commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function

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We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.

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function y = admin(z)
y = 1./z
return

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Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,

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ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation

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Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:
MATLAB Used

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Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation

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Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield

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3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?

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If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.

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7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?

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An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application

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Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD

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GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 15

(b) Verify the results using the MATLAB program.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');

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D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;

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x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);

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inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of

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1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:

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%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');

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dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;

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c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);

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Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);

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Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;

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Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)

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GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19



1. What is meant by geometric mean distance?

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GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?

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transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The

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high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.

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6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.

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Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such

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as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.

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11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor

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Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:

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Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.

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Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit

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3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?

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The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network

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Software required:
MATLAB 7.6
Theory:
Formation of Y
bus

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matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.

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Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful

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in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing

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buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:

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Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:

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(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03

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2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01

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4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....

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clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...

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tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...

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y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);

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ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch

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if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end

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ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using

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MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.

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3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?

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Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method

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8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?

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1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates

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the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:

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1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.

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(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce

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Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant

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3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.

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5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?

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Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the

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governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:

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A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625

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damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec

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The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).

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Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?

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Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?

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Frequency control loop
Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS

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SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=

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0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both

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lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program


Result:

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Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37



1. What is meant by stability?

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Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively

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large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network

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4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.

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6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of

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synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.

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A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and

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without line losses
Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:

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Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)

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, PG 2
(k)
, ?PG N
(K)
}; k = 1,2,? .... N S

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Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program

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Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.

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5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;

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P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost

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in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;
warning off;

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a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;

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lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001

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iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;

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disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda
p

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10

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lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000

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p =
400.0000
250.0000
150.0000
Total cost = 6.6825e+003

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Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW

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C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2

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; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW

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Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc
n=3;

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demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n

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x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n

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Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg
for i=1:n

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if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);

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else
Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);

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end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;

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y1=0;
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for i=2:n
x1=x1+(b(i)/(2*a(i)));

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y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));

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end
end
end
Pg
Output:

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lambda =
8.6149
Pg =
367.4040 379.4361 178.1598
Pg =

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350.0000 379.4361 178.1598
Demand new =
575
Lambda new =
8.7147

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Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.

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Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch

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Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment

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Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.

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Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?

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Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI

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MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:

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MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.

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(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1

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- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:

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For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)

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Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:

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By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?

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Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of

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variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

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FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

LABORATORY MANUAL

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

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ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

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3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

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CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

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12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

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Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

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tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

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? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

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MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

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1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

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M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

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series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

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methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

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has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

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helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

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commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

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positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

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command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

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>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

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in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

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>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

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>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

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>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

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>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

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Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

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>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;

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>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);

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>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a

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pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some

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input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?

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z= [5 2 4;
1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;

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1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;

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1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2

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Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.

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Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics

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Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming

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in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations

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4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?

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Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i

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8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.

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10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?

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Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?

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Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and

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double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1

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A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 15

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');

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d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))

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fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit
%3 phase double circuit

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S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');

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S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;

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b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);

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Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);

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Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);

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DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km

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C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:

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Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.

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2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines

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also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling

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5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically

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used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.

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8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?

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When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission

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line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.

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Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.

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Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load

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2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.

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4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?

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1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6

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Theory:
Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every

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transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus

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matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance

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matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:

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Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)

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Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.

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(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02

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1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02

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2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')

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fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...

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x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...

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nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end

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% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);

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end
end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix

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zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis

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Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27


1. What is meant by singular transformation method?

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The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.

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4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?

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loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance

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9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus

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11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.

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4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec

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Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with

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and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:

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To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple

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generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop

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7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the

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AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA

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POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram

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4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

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Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4

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Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in

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area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34


Application:

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To maintain the power and frequency constant in electrical power system.



1. What is meant by two area system?

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power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant

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3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop
Current control loop

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5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

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Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.

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(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:

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A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =

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0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.

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Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically

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the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system

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3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is

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the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its

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stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?

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The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The

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angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING

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MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:

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MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the

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total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2
(k)

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, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.

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This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda

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Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

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Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;

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P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:

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clc;
clear all;
warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];

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c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')

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disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);

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delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;

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end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000

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8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =
400.0000

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250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2

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; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:

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200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:

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clear
clc
n=3;
demand=925;
a=[.0056 .0045 .0079];

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b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];
Pmin=[200 250 125];

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Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));

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lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);

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end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);

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else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);

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end
end
Pgtotal=sum(Pg);
end
Pg

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if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

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for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end

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lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end

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end
Pg
Output:
lambda =
8.6149

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Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598
Demand new =

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575
Lambda new =
8.7147
Pg =
350.0000 390.5242 184.4758

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Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and

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without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:

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Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints

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2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints

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4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price

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6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?

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Minimum load Base load in power system
9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

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To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:
MATLAB 7.6
Theory:

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Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may

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come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small

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disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run

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5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system

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modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system

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for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.

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(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;

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X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;

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eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce
Result:

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Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming

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Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

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4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

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6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

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Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple

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method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow

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or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-

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scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to

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find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix

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Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0

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Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
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Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2

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Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec

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Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.

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(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b

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4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY

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ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-

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Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1

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=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were

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analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?

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The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a

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power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging

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with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle

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The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?

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9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:

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To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6
Theory:

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Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1

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(k)
, PG 2
(k)
, ?PG N
(K)

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}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:

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Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.

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4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;

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warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;

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delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;

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while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));

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dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda

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p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:

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Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =

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8.5000
p =
400.0000
250.0000
150.0000

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Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2

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; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW

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100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc

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n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;

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for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;

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for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg

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for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))

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Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end
end

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Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)

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x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n

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x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n

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Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end
end
Pg

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Output:
lambda =
8.6149
Pg =
367.4040 379.4361 178.1598

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Pg =
350.0000 379.4361 178.1598
Demand new =
575
Lambda new =

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8.7147
Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were

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obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:
Used in power system with lowest cost and schedule with generating unit

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1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.

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3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint

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5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints

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7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:

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Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not

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included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:

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- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

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Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)

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For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.

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Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.

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2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve

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The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle

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Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-

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SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:

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MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and

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phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &

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steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;

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Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate

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sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));

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Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else
Q(i)= Q max(i)

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Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program

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Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run

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5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor

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values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION

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VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

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deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

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? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

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MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals

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To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and

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training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism

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To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,

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through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field

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b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems

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e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility

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i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.

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4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems

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9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.

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2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.

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6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi

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machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.

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12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS

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1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26

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6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41

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10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 6

Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems

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Software required:
MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and

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programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.

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1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization

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? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small

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and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit

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(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,

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where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing

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them.
M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be

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called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace

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>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more

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generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the

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Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators

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2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)

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Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?

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>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in

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the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the

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workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence

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of commands
>>a=2;
>>b=5;
>>whos
>>clear all

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The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any

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DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is

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concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are

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considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,

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whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B

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Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)

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1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;

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>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];

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>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just

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>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if

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>>help for
>>help while
Example :

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]Looping :


>>if z=0
>>y=0

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>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:

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MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.

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>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)

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To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);

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The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The

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commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function

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We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.

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function y = admin(z)
y = 1./z
return

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Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,

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ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation

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Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:
MATLAB Used

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Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation

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Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield

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3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?

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If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.

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7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?

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An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application

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Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD

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GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');

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D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;

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x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);

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inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of

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1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:

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%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');

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dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;

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c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);

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Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);

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Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;

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Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)

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GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19



1. What is meant by geometric mean distance?

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GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?

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transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The

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high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.

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6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.

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Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such

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as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.

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11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor

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Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:

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Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.

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Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit

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3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?

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The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network

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Software required:
MATLAB 7.6
Theory:
Formation of Y
bus

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matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.

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Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful

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in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing

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buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:

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Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:

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(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03

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2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01

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4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....

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clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...

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tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...

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y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);

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ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch

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if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end

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ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using

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MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.

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3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?

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Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method

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8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?

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1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates

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the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:

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1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.

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(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce

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Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant

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3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.

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5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?

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Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the

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governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:

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A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625

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damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec

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The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).

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Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?

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Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?

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Frequency control loop
Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS

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SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=

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0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both

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lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program


Result:

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Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37



1. What is meant by stability?

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Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively

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large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network

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4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.

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6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of

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synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.

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A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and

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without line losses
Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:

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Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)

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, PG 2
(k)
, ?PG N
(K)
}; k = 1,2,? .... N S

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Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program

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Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.

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5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;

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P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost

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in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;
warning off;

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a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;

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lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001

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iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;

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disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda
p

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10

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lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000

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p =
400.0000
250.0000
150.0000
Total cost = 6.6825e+003

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Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW

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C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2

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; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW

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Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc
n=3;

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demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n

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x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n

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Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg
for i=1:n

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if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);

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else
Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);

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end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;

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y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n
x1=x1+(b(i)/(2*a(i)));

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y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));

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end
end
end
Pg
Output:

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lambda =
8.6149
Pg =
367.4040 379.4361 178.1598
Pg =

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350.0000 379.4361 178.1598
Demand new =
575
Lambda new =
8.7147

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Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.

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Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch

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Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment

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Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.

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Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?

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Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI

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MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:

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MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.

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(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1

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- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:

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For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)

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Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:

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By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?

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Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of

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variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

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Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD

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Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6

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Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power

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systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.

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[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;

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Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)

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Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop

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If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else
Q(i)= Q max(i)
Step 9: Check the condition for type

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V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:

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1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results

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Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using

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MATLAB.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:

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clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')

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nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);

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k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);

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Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];

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V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;
for i=1:nb
Pg=PG(i);

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Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;
end

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if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION

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VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

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deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

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? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

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MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals

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To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and

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training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism

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To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,

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through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field

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b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems

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e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility

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i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.

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4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems

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9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.

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2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.

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6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi

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machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.

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12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS

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1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26

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6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41

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10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68

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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems

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Software required:
MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and

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programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.

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1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization

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? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small

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and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit

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(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,

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where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing

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them.
M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be

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called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace

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>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more

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generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the

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Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators

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2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)

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Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?

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>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in

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the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the

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workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence

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of commands
>>a=2;
>>b=5;
>>whos
>>clear all

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The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any

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DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is

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concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are

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considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,

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whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B

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Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)

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1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;

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>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];

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>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just

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>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if

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>>help for
>>help while
Example :

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]Looping :


>>if z=0
>>y=0

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>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:

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MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.

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>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)

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To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);

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The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The

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commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function

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We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.

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function y = admin(z)
y = 1./z
return

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Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,

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ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation

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Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:
MATLAB Used

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Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation

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Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield

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3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?

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If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.

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7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?

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An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application

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Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD

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GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');

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D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;

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x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);

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inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of

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1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:

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%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');

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dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;

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c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);

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Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);

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Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;

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Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)

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GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19



1. What is meant by geometric mean distance?

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GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?

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transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The

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high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.

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6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.

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Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such

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as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.

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11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor

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Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:

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Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.

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Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit

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3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?

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The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network

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Software required:
MATLAB 7.6
Theory:
Formation of Y
bus

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matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.

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Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful

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in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing

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buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:

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Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:

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(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03

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2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01

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4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....

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clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...

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tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...

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y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);

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ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch

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if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end

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ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using

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MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.

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3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?

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Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method

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8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?

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1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates

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the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:

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1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.

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(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce

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Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant

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3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.

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5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?

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Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the

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governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:

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A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625

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damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec

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The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).

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Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?

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Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?

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Frequency control loop
Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS

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SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=

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0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both

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lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program


Result:

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Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37



1. What is meant by stability?

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Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively

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large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network

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4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.

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6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of

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synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.

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A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and

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without line losses
Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:

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Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)

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, PG 2
(k)
, ?PG N
(K)
}; k = 1,2,? .... N S

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Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program

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Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.

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5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;

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P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost

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in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;
warning off;

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a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;

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lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001

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iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;

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disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda
p

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10

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lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000

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p =
400.0000
250.0000
150.0000
Total cost = 6.6825e+003

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Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW

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C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2

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; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW

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Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc
n=3;

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demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n

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x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n

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Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg
for i=1:n

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if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);

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else
Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);

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end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;

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y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n
x1=x1+(b(i)/(2*a(i)));

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y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));

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end
end
end
Pg
Output:

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lambda =
8.6149
Pg =
367.4040 379.4361 178.1598
Pg =

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350.0000 379.4361 178.1598
Demand new =
575
Lambda new =
8.7147

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Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.

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Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch

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Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment

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Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.

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Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?

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Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI

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MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:

--- Content provided by FirstRanker.com ---

MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.

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(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1

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- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:

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For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)

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Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:

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By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?

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Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of

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variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

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Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD

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Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6

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Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power

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systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.

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[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;

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Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)

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Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop

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If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else
Q(i)= Q max(i)
Step 9: Check the condition for type

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V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:

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1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results

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Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using

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MATLAB.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:

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clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')

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nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);

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k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);

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Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];

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V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;
for i=1:nb
Pg=PG(i);

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Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;
end

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if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);
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end
B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);
end

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c=V(p)*(A+B);
Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;

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Vt(p)=V(p);
else
if(Q<=Qmin)
Q=Qmin;
else

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Q=Qmax;
end
Vt(p)=1;
disp('it is load bus')
Qg=Q*j

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end
QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);
end

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B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));

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Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 16

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2

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Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec

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Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.

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(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b

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4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY

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ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-

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Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1

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=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were

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analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?

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The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a

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power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging

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with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle

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The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?

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9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:

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To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6
Theory:

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Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1

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(k)
, PG 2
(k)
, ?PG N
(K)

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}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:

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Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.

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4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;

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warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;

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delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;

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while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));

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dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda

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p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:

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Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =

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8.5000
p =
400.0000
250.0000
150.0000

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Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2

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; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW

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100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc

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n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;

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for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;

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for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg

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for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))

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Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end
end

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Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)

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x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n

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x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n

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Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end
end
Pg

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Output:
lambda =
8.6149
Pg =
367.4040 379.4361 178.1598

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Pg =
350.0000 379.4361 178.1598
Demand new =
575
Lambda new =

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8.7147
Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were

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obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:
Used in power system with lowest cost and schedule with generating unit

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1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.

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3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint

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5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints

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7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:

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Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not

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included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:

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- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

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Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)

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For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.

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Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.

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2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve

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The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle

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Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

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Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-

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SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:

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MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and

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phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &

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steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;

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Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate

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sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));

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Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else
Q(i)= Q max(i)

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Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program

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Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run

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5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor

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values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Program:
clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')

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nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
PG=[0 .5 .4 .2];

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QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;
for i=1:nb

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Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;

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end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);
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end
B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);

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end
c=V(p)*(A+B);
Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt

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Qg=Q*j;
Vt(p)=V(p);
else
if(Q<=Qmin)
Q=Qmin;

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else
Q=Qmax;
end
Vt(p)=1;
disp('it is load bus')

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Qg=Q*j
end
QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);

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end
B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end

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C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1

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A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;

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for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))

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end
p=p+1;
end
Output:
Y bus =

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2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i

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Q =
0.1456, it is load bus
Q g =
0 + 0.1200i

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V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles

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FirstRanker.com - FirstRanker's Choice
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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :

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Register No. :
Class :

LABORATORY MANUAL
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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and

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soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING

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To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and

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ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education

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2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables

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them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context

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5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)

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a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical

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and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large

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h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines

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2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System

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7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance

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matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.

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8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.

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11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.

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14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS

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Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19

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4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS

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8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58

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Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB

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Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:

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1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and

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communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development

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? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical

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manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:

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To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.

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Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file

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M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined

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function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.

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>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic

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equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.

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>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common

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data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.

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1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is

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>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;

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>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands

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and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];

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>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A

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Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];

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(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;

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Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:

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>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];

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>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.

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>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,

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element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.

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To explore these simply type
>>help if
>>help for
>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end

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- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);

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To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)

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>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.

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1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s

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usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;

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1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.

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To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)

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y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]

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>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available

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in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:

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Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping

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Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

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2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?

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For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi

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domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?

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poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?

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Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,

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12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application

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development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:

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Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of

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D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have

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a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:

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%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');

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r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 16

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);

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fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2

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A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various

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cases.
Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');

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H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);

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a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;

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c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);

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Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);

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DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;

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GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);

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DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km

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Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double

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circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?

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GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.

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4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?

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A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight

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and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?

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9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-

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section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load

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is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE

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PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).

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Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:

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Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?

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Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?

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The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?

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2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:

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Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element

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corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:

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In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can

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be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.

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Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)

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Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.

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5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02

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1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025

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3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')

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linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...

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b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...

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nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...

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for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....

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for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end

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end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus

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Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus

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admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27


1. What is meant by singular transformation method?
The matrix formed by graph theory.

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2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?

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Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.

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7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?

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Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.

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Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA

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POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:

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MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power

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supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.

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5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit

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The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2

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sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?

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Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load

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4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?

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frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM

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Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:

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MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.

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A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram

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5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

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Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA

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Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.

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(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and

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without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34


Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet

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the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?

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a and b
4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

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Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:

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To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:

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Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may

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come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small

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disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run

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5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d

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1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:

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By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact

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2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?

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The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability

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5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.

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7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more

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than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB

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Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6

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Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules

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{PG 1
(k)
, PG 2
(k)
, ?PG N

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(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.

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Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution

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Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File

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3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

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Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW

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C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2

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; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;

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clear all;
warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];

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Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])

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iter=0;
while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);

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J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end

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lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)

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Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0

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lambda =
8.5000
p =
400.0000
250.0000

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150.0000
Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1

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2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW

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C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW

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150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear

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clc
n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];

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x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y

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Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end

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Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else

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if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end

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end
Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand

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demandnew=demand-Pg(1)
x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

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for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1

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for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end
end

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Pg
Output:
lambda =
8.6149
Pg =

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367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598
Demand new =
575

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Lambda new =
8.7147
Pg =
350.0000 390.5242 184.4758
Result:

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Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:
Used in power system with lowest cost and schedule with generating unit

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1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?

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lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?

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Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?

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objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system

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9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)

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system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:

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I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds

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(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

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Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;

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eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained

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using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:

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Used to analysis to transient and steady state behavior of generator.



1. What is meant by steady state stability?

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power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

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4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

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6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

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Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm

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Software required:
MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best

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operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,

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computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,

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P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop

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if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else

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Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)

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Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window

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4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances

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are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Program:
clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')

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eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);

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for i=1:nl
k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);

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Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus

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PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;

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for i=1:nb
Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;

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Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);

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end
B=0;
for q=p:nb

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B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);
Q=-imag(c)

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if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);
else
if(Q<=Qmin)

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Q=Qmin;
else
Q=Qmax;
end
Vt(p)=1;

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disp('it is load bus')
Qg=Q*j
end
QG(p)=Qg;
for q=1:p-1

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A1=Ybus(p,q)*V(q);
end
B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));

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end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;

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for q=1:p-1
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A2=A2-Ybus(p,q)*Vt(q);
end

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B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end
C2=(-PG(p)+(QG(p))/V(p));

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Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;
end
Output:

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Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i

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Q =
0.1456, it is load bus
Q g =

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0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power

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flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

Application:

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Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the

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acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus

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The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6

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7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement
Less computational time per iteration
8. List the advantages of load flow analysis.

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Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

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z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
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VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

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communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y

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capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase

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per Kilometer of the line.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit

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%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;

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Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;

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a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);

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Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);

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Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);

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DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)

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L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving

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parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture

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when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next

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physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.

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This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?

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Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several

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advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.

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10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?

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In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:

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To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.

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Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium

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transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?

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Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?

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Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.

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6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND

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IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:

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MATLAB 7.6
Theory:
Formation of Y
bus
matrix:

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Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z

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bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.

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The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.

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Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)

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Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.

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(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus

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1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01

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2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04

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5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....
clc

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fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...

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r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...

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b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));

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end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m

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ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end
ybus = ybus % Bus Admittance Matrix

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zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:

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Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?

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Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view

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6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?

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Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm

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2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power

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system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.

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3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:

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Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady

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state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink

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Application:
To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?

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If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?

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In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?

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Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop

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Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power

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system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model

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3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9

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Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is

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computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the

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frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop

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Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:

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MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are

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marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.

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b) Verify the result using MATLAB program


Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)

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system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of

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operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.

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is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time

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The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time

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The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism

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8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.

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Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses

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Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:

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In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2

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(k)
, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which

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minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma

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Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1

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2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW

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C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.

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Program:
clc;
clear all;
warning off;
a=[.004; .006; .009];

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b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');

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fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;

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p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])

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lambda=lambda+dellambda;
end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda

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10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =

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400.0000
250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.

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Program:
clear
clc
n=3;
demand=925;

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a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];

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Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));

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y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));

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Pgtotal=sum(Pg);
end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));

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Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else

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Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);
end

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Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));

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end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end

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end
end
Pg
Output:
lambda =

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8.6149
Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598

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Demand new =
575
Lambda new =
8.7147
Pg =

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350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:

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By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to

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meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to

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device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit

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Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch

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8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of

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system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

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To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.

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2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:

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1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.

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Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed

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- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:
For (a)

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Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;

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X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce

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Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)

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system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances

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3. Write the swing equation in a power system.

4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances

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5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:

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To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6
Theory:

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The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers

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were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]

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In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Get the input Value

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Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop

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For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)

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Q(i)<=Q min(i)
Else
Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);

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Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB

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2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:

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The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:
clc

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clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')

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sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i) ;

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y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);

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end
Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];

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Qmin=.05;
Qmax=.12;
for i=1:nb
Pg=PG(i);
Qg=QG(i);

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if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus

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for q=1:p-1
A=Ybus(p,q)*V(q);
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end

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B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);

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Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);

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else
if(Q<=Qmin)
Q=Qmin;
else
Q=Qmax;

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end
Vt(p)=1;
disp('it is load bus')
Qg=Q*j
end

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QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);
end
B1=0;

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for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));

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elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1
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A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));

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end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;

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end
Output:
Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i

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-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i


Q =

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0.1456, it is load bus
Q g =
0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i

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Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

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Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded

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2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,

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controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus

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6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement

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Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus

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10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method

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Software required:
MATLAB 7.6
Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are

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limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-

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scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,

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some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6

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Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation

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Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max
End the Loop
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 16

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2

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Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec

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Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.

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(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b

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4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY

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ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-

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Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1

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=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were

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analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?

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The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a

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power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging

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with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle

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The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?

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9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:

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To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6
Theory:

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Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1

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(k)
, PG 2
(k)
, ?PG N
(K)

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}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:

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Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.

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4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;

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warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;

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delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;

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while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));

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dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda

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p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:

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Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =

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8.5000
p =
400.0000
250.0000
150.0000

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Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2

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; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW

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100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc

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n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;

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for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;

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for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg

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for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))

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Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end
end

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Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)

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x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n

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x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n

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Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end
end
Pg

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Output:
lambda =
8.6149
Pg =
367.4040 379.4361 178.1598

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Pg =
350.0000 379.4361 178.1598
Demand new =
575
Lambda new =

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8.7147
Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were

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obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:
Used in power system with lowest cost and schedule with generating unit

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1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.

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3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint

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5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints

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7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:

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Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not

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included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:

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- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

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Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)

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For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.

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Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.

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2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve

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The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle

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Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-

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SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:

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MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and

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phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &

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steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;

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Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate

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sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));

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Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else
Q(i)= Q max(i)

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Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program

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Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run

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5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor

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values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Program:
clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')

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nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
PG=[0 .5 .4 .2];

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QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;
for i=1:nb

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Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;

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end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);
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end
B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);

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end
c=V(p)*(A+B);
Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt

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Qg=Q*j;
Vt(p)=V(p);
else
if(Q<=Qmin)
Q=Qmin;

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else
Q=Qmax;
end
Vt(p)=1;
disp('it is load bus')

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Qg=Q*j
end
QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);

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end
B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end

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C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1

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A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;

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for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))

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end
p=p+1;
end
Output:
Y bus =

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2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i

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Q =
0.1456, it is load bus
Q g =
0 + 0.1200i

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V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles

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1. What is meant by load flow analysis?

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Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor

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3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators

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5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.

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Simplicity in technique
Small computer memory requirement
Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses

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9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.

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Viva - voce
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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD

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Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:
MATLAB 7.6
Theory:

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The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive

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power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.

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[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate

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P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max

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End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

Step 7: Change from specified Value
Declare dPa= Psp-P

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dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1

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Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses

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Step 13: Display the output
Step 14: End the Program
Exercise:

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FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

LABORATORY MANUAL

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

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ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

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3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

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CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

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12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

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Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

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tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

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? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

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MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

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1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

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M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

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series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

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methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

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has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

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helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

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commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

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positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

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command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

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>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

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in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

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>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

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>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

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>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

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>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

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Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

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>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;

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>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);

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>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a

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pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some

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input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?

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z= [5 2 4;
1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;

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1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;

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1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2

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Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.

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Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics

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Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming

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in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations

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4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?

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Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i

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8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.

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10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?

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Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?

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Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and

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double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1

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A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');

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d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))

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fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit
%3 phase double circuit

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S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');

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S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;

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b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);

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Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);

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Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);

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DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km

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C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:

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Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.

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2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines

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also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling

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5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically

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used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.

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8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?

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When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission

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line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.

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Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.

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Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load

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2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.

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4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?

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1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6

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Theory:
Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every

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transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus

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matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance

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matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:

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Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)

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Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.

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(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02

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1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02

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2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')

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fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...

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x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...

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nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end

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% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);

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end
end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix

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zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis

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Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27


1. What is meant by singular transformation method?

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The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.

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4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?

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loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance

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9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus

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11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.

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4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec

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Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with

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and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:

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To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple

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generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop

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7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the

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AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA

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POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram

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4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

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Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4

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Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in

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area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34


Application:

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To maintain the power and frequency constant in electrical power system.



1. What is meant by two area system?

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power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant

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3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop
Current control loop

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5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

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Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.

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(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:

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A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =

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0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.

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Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically

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the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system

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3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is

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the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its

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stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?

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The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The

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angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING

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MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:

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MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the

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total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2
(k)

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, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.

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This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda

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Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

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Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;

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P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:

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clc;
clear all;
warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];

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c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')

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disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);

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delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;

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end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000

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8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =
400.0000

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250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2

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; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:

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200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:

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clear
clc
n=3;
demand=925;
a=[.0056 .0045 .0079];

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b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];
Pmin=[200 250 125];

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Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));

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lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);

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end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);

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else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);

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end
end
Pgtotal=sum(Pg);
end
Pg

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if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

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for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end

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lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end

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end
Pg
Output:
lambda =
8.6149

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Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598
Demand new =

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575
Lambda new =
8.7147
Pg =
350.0000 390.5242 184.4758

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Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and

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without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:

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Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints

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2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints

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4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price

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6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?

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Minimum load Base load in power system
9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

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To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:
MATLAB 7.6
Theory:

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Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may

--- Content provided by FirstRanker.com ---

come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small

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disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run

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5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system

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modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system

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for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.

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(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;

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X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;

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eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce
Result:

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Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming

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Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

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4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

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6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

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Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple

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method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow

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or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-

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scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to

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find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix

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Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0

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Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)

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Else
Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented

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Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.

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3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude

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at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:
clc
clear all

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sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')

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Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);

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Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end

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Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;

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Qmax=.12;
for i=1:nb
Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus

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p=1;
Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1

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A=Ybus(p,q)*V(q);
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end
B=0;

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for q=p:nb
B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);
Q=-imag(c)

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if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);
else

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if(Q<=Qmin)
Q=Qmin;
else
Q=Qmax;
end

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Vt(p)=1;
disp('it is load bus')
Qg=Q*j
end
QG(p)=Qg;

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for q=1:p-1
A1=Ybus(p,q)*V(q);
end
B1=0;
for q=p+1:nb

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B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus

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A2=0;
for q=1:p-1
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A2=A2-Ybus(p,q)*Vt(q);

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end
B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end

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C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;
end

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Output:
Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i

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0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i


Q =
0.1456, it is load bus

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Q g =
0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:

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Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

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Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52

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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?

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Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage

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4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?

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acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement
Less computational time per iteration

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8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

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z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:

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MATLAB 7.6
Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of

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power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical

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solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per

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kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max

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Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2

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Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max
End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

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Step 7: Change from specified Value
Declare dPa= Psp-P
dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3

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End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2

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Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses
Step 13: Display the output
Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

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1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus
Real load
demand, P D

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Reactive Load
demand, Q D
Real power
Generation, P G
Reactive Power

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Generation, Q G
Voltage
Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified

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3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD

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clc
clear all
sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')

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nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);

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k2=eb(i);
y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);

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Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);

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% Calculation of P and Q
v=[1.06 1 1];
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

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communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13


1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 15

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y

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capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase

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per Kilometer of the line.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit

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%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;

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Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;

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a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);

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Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);

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Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);

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DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)

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L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving

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parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture

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when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next

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physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.

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This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?

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Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several

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advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.

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10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?

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In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:

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To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.

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Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium

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transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?

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Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?

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Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.

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6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND

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IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:

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MATLAB 7.6
Theory:
Formation of Y
bus
matrix:

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Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z

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bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.

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The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.

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Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)

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Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.

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(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus

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1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01

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2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04

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5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....
clc

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fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...

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r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...

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b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));

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end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m

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ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end
ybus = ybus % Bus Admittance Matrix

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zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:

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Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?

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Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view

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6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?

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Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm

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2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power

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system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.

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3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:

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Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady

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state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink

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Application:
To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?

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If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?

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In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?

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Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop

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Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power

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system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model

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3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9

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Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is

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computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the

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frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop

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Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:

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MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are

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marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.

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b) Verify the result using MATLAB program


Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)

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system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of

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operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.

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is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time

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The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time

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The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism

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8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.

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Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses

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Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:

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In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2

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(k)
, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which

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minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma

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Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1

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2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW

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C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.

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Program:
clc;
clear all;
warning off;
a=[.004; .006; .009];

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b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');

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fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;

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p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])

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lambda=lambda+dellambda;
end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda

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10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =

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400.0000
250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.

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Program:
clear
clc
n=3;
demand=925;

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a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];

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Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));

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y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));

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Pgtotal=sum(Pg);
end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));

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Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else

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Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);
end

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Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));

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end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end

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end
end
Pg
Output:
lambda =

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8.6149
Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598

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Demand new =
575
Lambda new =
8.7147
Pg =

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350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:

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By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to

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meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to

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device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit

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Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch

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8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of

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system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

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To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.

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2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:

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1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.

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Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed

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- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:
For (a)

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Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;

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X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce

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Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)

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system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances

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3. Write the swing equation in a power system.

4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances

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5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:

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To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6
Theory:

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The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers

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were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]

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In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Get the input Value

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Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop

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For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)

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Q(i)<=Q min(i)
Else
Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);

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Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB

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2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:

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The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:
clc

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clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')

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sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i) ;

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y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);

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end
Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];

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Qmin=.05;
Qmax=.12;
for i=1:nb
Pg=PG(i);
Qg=QG(i);

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if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus

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for q=1:p-1
A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

end

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B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);

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Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);

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else
if(Q<=Qmin)
Q=Qmin;
else
Q=Qmax;

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end
Vt(p)=1;
disp('it is load bus')
Qg=Q*j
end

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QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);
end
B1=0;

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for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));

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elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

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A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));

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end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;

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end
Output:
Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i

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-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i


Q =

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0.1456, it is load bus
Q g =
0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i

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Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

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Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52

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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded

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2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,

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controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus

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6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement

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Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus

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10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method

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Software required:
MATLAB 7.6
Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are

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limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-

--- Content provided by FirstRanker.com ---

scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,

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some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6

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Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation

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Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max
End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

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Step 7: Change from specified Value
Declare dPa= Psp-P
dQa= Qsp- Q
dQ= Zeros(npq,1)

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Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with

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angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses
Step 13: Display the output
Step 14: End the Program

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Exercise:



Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

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1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus
Real load

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demand, P D
Reactive Load
demand, Q D
Real power
Generation, P G

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Reactive Power
Generation, Q G
Voltage
Specified
1 2 1 - - V 1=1.04

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2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

2. Verify the result using MATLAB
Program:

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%NEWTON RAPHSON METHOD
clc
clear all
sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')

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nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i);
y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
Ybusmag=abs(Ybus);

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Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q
v=[1.06 1 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

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P=[0 0 0];
Q=[0 0 0];
del=[0 0 0];
Pg=[0 0.2 0];
Pd=[0 0 0.6];

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Qg=[0 0 0];
Qd=[0 0 0.25];
for p=2:nb
for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));

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Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);
delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);

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end
end
P;
Q;
Pspe;

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Qspe;
delP;
delQ;

%Calculation of J1

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P2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));

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for j=1:nb
if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));
PV(p,q)=P1+P2(q);
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2

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Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec

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Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.

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(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b

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4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY

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ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-

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Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1

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=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were

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analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?

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The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a

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power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging

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with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle

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The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?

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9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:

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To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6
Theory:

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Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1

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(k)
, PG 2
(k)
, ?PG N
(K)

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}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:

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Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.

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4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;

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warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;

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delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;

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while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));

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dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda

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p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:

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Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =

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8.5000
p =
400.0000
250.0000
150.0000

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Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2

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; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW

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100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc

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n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;

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for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;

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for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg

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for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))

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Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end
end

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Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)

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x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n

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x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n

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Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end
end
Pg

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Output:
lambda =
8.6149
Pg =
367.4040 379.4361 178.1598

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Pg =
350.0000 379.4361 178.1598
Demand new =
575
Lambda new =

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8.7147
Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were

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obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:
Used in power system with lowest cost and schedule with generating unit

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1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.

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3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint

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5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints

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7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:

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Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not

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included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:

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- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

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Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)

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For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.

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Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.

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2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve

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The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle

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Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-

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SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:

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MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and

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phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &

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steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;

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Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate

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sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));

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Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else
Q(i)= Q max(i)

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Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program

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Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run

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5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor

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values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

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Program:
clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')

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nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
PG=[0 .5 .4 .2];

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QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;
for i=1:nb

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Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;

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end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

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end
B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);

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end
c=V(p)*(A+B);
Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt

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Qg=Q*j;
Vt(p)=V(p);
else
if(Q<=Qmin)
Q=Qmin;

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else
Q=Qmax;
end
Vt(p)=1;
disp('it is load bus')

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Qg=Q*j
end
QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);

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end
B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end

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C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;

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for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))

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end
p=p+1;
end
Output:
Y bus =

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2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i

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Q =
0.1456, it is load bus
Q g =
0 + 0.1200i

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V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52



1. What is meant by load flow analysis?

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Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor

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3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators

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5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.

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Simplicity in technique
Small computer memory requirement
Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses

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9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD

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Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:
MATLAB 7.6
Theory:

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The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive

--- Content provided by FirstRanker.com ---

power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.

--- Content provided by FirstRanker.com ---

[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate

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P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max

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End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

Step 7: Change from specified Value
Declare dPa= Psp-P

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dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1

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Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses

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Step 13: Display the output
Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.

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Bus
Real load
demand, P D
Reactive Load
demand, Q D

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Real power
Generation, P G
Reactive Power
Generation, Q G
Voltage

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Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

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2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD
clc
clear all

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sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')

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Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i);
y(i)=(sa(i));

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Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end

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Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q
v=[1.06 1 1];

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

P=[0 0 0];
Q=[0 0 0];
del=[0 0 0];

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Pg=[0 0.2 0];
Pd=[0 0 0.6];
Qg=[0 0 0];
Qd=[0 0 0.25];
for p=2:nb

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for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);

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delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);
end
end
P;

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Q;
Pspe;
Qspe;
delP;
delQ;

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%Calculation of J1
P2=[0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb
if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));

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PV(p,q)=P1+P2(q);
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end
end

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else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end

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PV;
% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
for j=1:nb
if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end

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end
else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end
end

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end
Pdel;
%Calculation of J3
Q2=[0 0 0];
for p=2:nb

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for q=2:nb
if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb
if (j~=p)

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Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
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VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

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communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13


1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y

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capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase

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per Kilometer of the line.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit

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%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;

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Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;

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a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);

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Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);

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Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);

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DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)

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L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving

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parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture

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when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next

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physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.

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This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?

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Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several

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advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.

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10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?

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In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:

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To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.

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Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium

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transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?

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Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?

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Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.

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6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND

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IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:

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MATLAB 7.6
Theory:
Formation of Y
bus
matrix:

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Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z

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bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.

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The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.

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Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)

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Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.

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(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus

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1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01

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2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04

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5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....
clc

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fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...

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r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...

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b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));

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end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m

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ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end
ybus = ybus % Bus Admittance Matrix

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zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:

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Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?

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Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view

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6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?

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Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm

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2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power

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system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.

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3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:

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Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady

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state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink

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Application:
To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?

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If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?

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In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?

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Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop

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Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power

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system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model

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3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9

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Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is

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computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the

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frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop

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Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:

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MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are

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marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.

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b) Verify the result using MATLAB program


Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)

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system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of

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operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.

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is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time

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The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time

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The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism

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8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.

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Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses

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Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:

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In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2

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(k)
, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which

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minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma

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Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1

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2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW

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C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.

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Program:
clc;
clear all;
warning off;
a=[.004; .006; .009];

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b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');

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fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;

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p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])

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lambda=lambda+dellambda;
end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda

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10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =

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400.0000
250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.

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Program:
clear
clc
n=3;
demand=925;

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a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];

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Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));

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y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));

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Pgtotal=sum(Pg);
end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));

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Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else

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Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);
end

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Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));

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end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end

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end
end
Pg
Output:
lambda =

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8.6149
Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598

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Demand new =
575
Lambda new =
8.7147
Pg =

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350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:

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By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to

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meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to

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device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit

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Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch

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8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of

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system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

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To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.

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2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:

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1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.

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Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed

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- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:
For (a)

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Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;

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X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce

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Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)

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system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances

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3. Write the swing equation in a power system.

4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances

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5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:

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To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6
Theory:

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The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers

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were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]

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In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Get the input Value

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Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop

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For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)

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Q(i)<=Q min(i)
Else
Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);

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Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB

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2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:

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The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:
clc

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clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')

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sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i) ;

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y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);

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end
Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];

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Qmin=.05;
Qmax=.12;
for i=1:nb
Pg=PG(i);
Qg=QG(i);

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if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus

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for q=1:p-1
A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

end

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B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);

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Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);

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else
if(Q<=Qmin)
Q=Qmin;
else
Q=Qmax;

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end
Vt(p)=1;
disp('it is load bus')
Qg=Q*j
end

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QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);
end
B1=0;

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for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));

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elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

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A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));

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end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;

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end
Output:
Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i

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-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i


Q =

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0.1456, it is load bus
Q g =
0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i

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Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

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Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded

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2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,

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controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus

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6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement

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Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus

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10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method

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Software required:
MATLAB 7.6
Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are

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limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-

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scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,

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some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6

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Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation

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Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max
End the Loop
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Step 7: Change from specified Value
Declare dPa= Psp-P
dQa= Qsp- Q
dQ= Zeros(npq,1)

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Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with

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angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses
Step 13: Display the output
Step 14: End the Program

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Exercise:



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1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus
Real load

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demand, P D
Reactive Load
demand, Q D
Real power
Generation, P G

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Reactive Power
Generation, Q G
Voltage
Specified
1 2 1 - - V 1=1.04

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2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

2. Verify the result using MATLAB
Program:

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%NEWTON RAPHSON METHOD
clc
clear all
sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')

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nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i);
y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
Ybusmag=abs(Ybus);

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Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q
v=[1.06 1 1];
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P=[0 0 0];
Q=[0 0 0];
del=[0 0 0];
Pg=[0 0.2 0];
Pd=[0 0 0.6];

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Qg=[0 0 0];
Qd=[0 0 0.25];
for p=2:nb
for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));

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Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);
delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);

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end
end
P;
Q;
Pspe;

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Qspe;
delP;
delQ;

%Calculation of J1

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P2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));

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for j=1:nb
if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));
PV(p,q)=P1+P2(q);
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end
end
else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
PV;
% Calculation of J2

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Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb

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if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end
end
else

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Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end
end
end
Pdel;

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%Calculation of J3
Q2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)

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Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb
if (j~=p)
Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);

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end
end
else

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QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));
end
end

end

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QV;
%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
for j=1:nb
if(j~=p)
Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end

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end
else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end

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end
Qdel;
%Jacobian matrix
PV(1,:)=[ ];
PV(:,1)=[ ];

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Pdel(1,:)=[ ];
Pdel(:,1)=[ ];
QV(1,:)=[ ];
QV(:,1)=[ ];
Qdel(1,:)=[ ];

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Qdel(:,1)=[ ];
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

LABORATORY MANUAL

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

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ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

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3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

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CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

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12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

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Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

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tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

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? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

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MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

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1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

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M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

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series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

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methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

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has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 8

4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

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helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

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commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

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positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

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command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

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>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

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in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

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>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

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>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

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>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

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>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

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Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

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>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;

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>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);

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>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a

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pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some

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input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?

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z= [5 2 4;
1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;

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1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;

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1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2

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Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.

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Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics

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Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming

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in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations

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4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?

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Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i

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8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.

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10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?

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Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?

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Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and

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double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1

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A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');

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d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))

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fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit
%3 phase double circuit

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S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');

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S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;

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b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);

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Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);

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Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);

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DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km

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C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:

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Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.

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2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines

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also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling

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5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically

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used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.

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8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?

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When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission

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line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.

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Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.

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Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load

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2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.

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4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?

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1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6

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Theory:
Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every

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transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus

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matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance

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matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:

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Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)

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Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.

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(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02

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1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02

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2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')

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fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...

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x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...

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nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end

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% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);

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end
end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix

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zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis

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Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27


1. What is meant by singular transformation method?

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The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.

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4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?

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loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance

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9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus

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11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.

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4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec

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Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with

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and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:

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To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple

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generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop

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7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the

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AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA

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POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram

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4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

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Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4

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Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in

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area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34


Application:

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To maintain the power and frequency constant in electrical power system.



1. What is meant by two area system?

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power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant

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3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop
Current control loop

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5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

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Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.

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(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:

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A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =

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0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.

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Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically

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the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system

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3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is

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the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its

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stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?

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The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The

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angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING

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MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:

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MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the

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total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2
(k)

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, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.

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This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda

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Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

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Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;

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P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:

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clc;
clear all;
warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];

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c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')

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disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);

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delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;

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end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000

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8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =
400.0000

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250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2

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; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:

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200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:

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clear
clc
n=3;
demand=925;
a=[.0056 .0045 .0079];

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b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];
Pmin=[200 250 125];

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Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));

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lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);

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end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);

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else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);

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end
end
Pgtotal=sum(Pg);
end
Pg

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if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

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for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end

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lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end

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end
Pg
Output:
lambda =
8.6149

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Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598
Demand new =

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575
Lambda new =
8.7147
Pg =
350.0000 390.5242 184.4758

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Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and

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without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:

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Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints

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2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints

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4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price

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6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?

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Minimum load Base load in power system
9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

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To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:
MATLAB 7.6
Theory:

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Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may

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come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small

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disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run

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5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system

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modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system

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for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.

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(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;

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X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;

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eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce
Result:

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Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming

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Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

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4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

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6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

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Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple

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method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow

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or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-

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scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to

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find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix

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Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0

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Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)

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Else
Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented

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Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.

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3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude

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at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:
clc
clear all

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sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')

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Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);

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Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end

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Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;

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Qmax=.12;
for i=1:nb
Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus

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p=1;
Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1

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A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

end
B=0;

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for q=p:nb
B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);
Q=-imag(c)

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if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);
else

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if(Q<=Qmin)
Q=Qmin;
else
Q=Qmax;
end

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Vt(p)=1;
disp('it is load bus')
Qg=Q*j
end
QG(p)=Qg;

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for q=1:p-1
A1=Ybus(p,q)*V(q);
end
B1=0;
for q=p+1:nb

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B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus

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A2=0;
for q=1:p-1
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

A2=A2-Ybus(p,q)*Vt(q);

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end
B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end

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C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;
end

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Output:
Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i

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0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i


Q =
0.1456, it is load bus

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Q g =
0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:

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Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

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Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52

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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?

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Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage

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4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?

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acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement
Less computational time per iteration

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8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

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z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:

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MATLAB 7.6
Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of

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power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical

--- Content provided by FirstRanker.com ---

solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per

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kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max

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Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2

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Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max
End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

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Step 7: Change from specified Value
Declare dPa= Psp-P
dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3

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End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2

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Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses
Step 13: Display the output
Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

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1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus
Real load
demand, P D

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Reactive Load
demand, Q D
Real power
Generation, P G
Reactive Power

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Generation, Q G
Voltage
Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified

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3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD

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clc
clear all
sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')

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nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);

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k2=eb(i);
y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);

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Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);

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% Calculation of P and Q
v=[1.06 1 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

P=[0 0 0];

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Q=[0 0 0];
del=[0 0 0];
Pg=[0 0.2 0];
Pd=[0 0 0.6];
Qg=[0 0 0];

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Qd=[0 0 0.25];
for p=2:nb
for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));

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Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);
delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);
end

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end
P;
Q;
Pspe;
Qspe;

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delP;
delQ;

%Calculation of J1
P2=[0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb

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if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));
PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

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end
end
else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end

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end
end
PV;
% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb
if(j~=p)

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Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end
end
else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
Pdel;
%Calculation of J3

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Q2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));

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for j=1:nb
if (j~=p)
Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 58

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end
end
else
QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));

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end
end

end
QV;

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%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb
if(p==q)

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for j=1:nb
if(j~=p)
Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end
end

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else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end

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Qdel;
%Jacobian matrix
PV(1,:)=[ ];
PV(:,1)=[ ];
Pdel(1,:)=[ ];

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Pdel(:,1)=[ ];
QV(1,:)=[ ];
QV(:,1)=[ ];
Qdel(1,:)=[ ];
Qdel(:,1)=[ ];

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 59

J=[PV Pdel;QV Qdel]
%Find the change in v&del
delP(1:1)=[];

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delQ(1:1)=[];
delpq=[delP';delQ']
vdel=inv(J)*delpq
%Find new v&del
for i=1:nb-1

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for j=2:nb
vnew(i)=v(j)+vdel(i);
delnew(i)=del(j)+vdel(i+2);
end
end

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VNEW=[v(1) vnew]
DELNEW=[del(1) delnew
Output:
Ybus =
6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i

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-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i
J =
2.8420 -1.6670 8.9750 -5.0000
-1.6670 6.3670 -5.0000 20.9000

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8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670
delpq =
0.2750
-0.3000

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0.2250
0.6500
vdel =
0.0575
0.0410

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0.0088
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

LABORATORY MANUAL

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

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ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

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3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

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CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

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12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

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Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

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tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

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? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

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MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

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1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

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M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

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series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

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methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

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has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

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helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

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commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

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positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

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command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

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>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

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in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

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>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

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>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

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>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

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>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

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Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

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>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;

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>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);

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>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a

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pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some

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input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?

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z= [5 2 4;
1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;

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1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;

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1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2

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Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.

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Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics

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Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming

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in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations

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4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?

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Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i

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8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.

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10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?

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Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?

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Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and

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double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1

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A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');

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d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))

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fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit
%3 phase double circuit

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S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');

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S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;

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b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);

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Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);

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Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);

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DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km

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C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:

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Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.

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2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines

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also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling

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5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically

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used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.

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8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?

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When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission

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line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.

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Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.

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Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load

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2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.

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4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?

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1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6

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Theory:
Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every

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transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus

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matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance

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matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:

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Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)

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Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.

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(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02

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1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02

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2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')

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fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...

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x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...

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nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end

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% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);

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end
end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix

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zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis

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Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27


1. What is meant by singular transformation method?

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The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.

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4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?

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loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance

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9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus

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11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.

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4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec

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Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with

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and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:

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To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple

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generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop

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7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the

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AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA

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POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram

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4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

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Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4

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Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in

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area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34


Application:

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To maintain the power and frequency constant in electrical power system.



1. What is meant by two area system?

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power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant

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3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop
Current control loop

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5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

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Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.

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(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:

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A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =

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0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.

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Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically

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the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system

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3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is

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the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its

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stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?

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The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The

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angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING

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MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:

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MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the

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total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2
(k)

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, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.

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This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda

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Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

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Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;

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P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:

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clc;
clear all;
warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];

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c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')

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disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);

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delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;

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end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000

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8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =
400.0000

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250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2

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; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:

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200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:

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clear
clc
n=3;
demand=925;
a=[.0056 .0045 .0079];

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b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];
Pmin=[200 250 125];

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Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));

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lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);

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end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);

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else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);

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end
end
Pgtotal=sum(Pg);
end
Pg

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if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

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for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end

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lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end

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end
Pg
Output:
lambda =
8.6149

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Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598
Demand new =

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575
Lambda new =
8.7147
Pg =
350.0000 390.5242 184.4758

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Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and

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without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:

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Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints

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2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints

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4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price

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6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?

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Minimum load Base load in power system
9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

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To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:
MATLAB 7.6
Theory:

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Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may

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come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small

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disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run

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5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system

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modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system

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for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.

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(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;

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X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;

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eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce
Result:

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Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming

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Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

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4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

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6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

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Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple

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method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow

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or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-

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scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to

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find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix

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Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0

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Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)

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Else
Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented

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Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.

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3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude

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at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:
clc
clear all

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sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')

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Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);

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Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end

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Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;

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Qmax=.12;
for i=1:nb
Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus

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p=1;
Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1

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A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

end
B=0;

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for q=p:nb
B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);
Q=-imag(c)

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if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);
else

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if(Q<=Qmin)
Q=Qmin;
else
Q=Qmax;
end

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Vt(p)=1;
disp('it is load bus')
Qg=Q*j
end
QG(p)=Qg;

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for q=1:p-1
A1=Ybus(p,q)*V(q);
end
B1=0;
for q=p+1:nb

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B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus

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A2=0;
for q=1:p-1
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

A2=A2-Ybus(p,q)*Vt(q);

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end
B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end

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C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;
end

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Output:
Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i

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0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i


Q =
0.1456, it is load bus

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Q g =
0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:

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Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

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Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52

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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?

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Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage

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4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?

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acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement
Less computational time per iteration

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8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

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z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:

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MATLAB 7.6
Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of

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power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical

--- Content provided by FirstRanker.com ---

solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per

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kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max

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Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2

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Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max
End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

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Step 7: Change from specified Value
Declare dPa= Psp-P
dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3

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End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2

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Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses
Step 13: Display the output
Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

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1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus
Real load
demand, P D

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Reactive Load
demand, Q D
Real power
Generation, P G
Reactive Power

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Generation, Q G
Voltage
Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified

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3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD

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clc
clear all
sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')

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nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);

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k2=eb(i);
y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);

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Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);

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% Calculation of P and Q
v=[1.06 1 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

P=[0 0 0];

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Q=[0 0 0];
del=[0 0 0];
Pg=[0 0.2 0];
Pd=[0 0 0.6];
Qg=[0 0 0];

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Qd=[0 0 0.25];
for p=2:nb
for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));

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Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);
delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);
end

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end
P;
Q;
Pspe;
Qspe;

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delP;
delQ;

%Calculation of J1
P2=[0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb

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if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));
PV(p,q)=P1+P2(q);
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end
end
else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end

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end
end
PV;
% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb
if(j~=p)

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Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end
end
else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
Pdel;
%Calculation of J3

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Q2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));

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for j=1:nb
if (j~=p)
Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);
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end
end
else
QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));

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end
end

end
QV;

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%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb
if(p==q)

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for j=1:nb
if(j~=p)
Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end
end

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else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end

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Qdel;
%Jacobian matrix
PV(1,:)=[ ];
PV(:,1)=[ ];
Pdel(1,:)=[ ];

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Pdel(:,1)=[ ];
QV(1,:)=[ ];
QV(:,1)=[ ];
Qdel(1,:)=[ ];
Qdel(:,1)=[ ];

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J=[PV Pdel;QV Qdel]
%Find the change in v&del
delP(1:1)=[];

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delQ(1:1)=[];
delpq=[delP';delQ']
vdel=inv(J)*delpq
%Find new v&del
for i=1:nb-1

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for j=2:nb
vnew(i)=v(j)+vdel(i);
delnew(i)=del(j)+vdel(i+2);
end
end

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VNEW=[v(1) vnew]
DELNEW=[del(1) delnew
Output:
Ybus =
6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i

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-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i
J =
2.8420 -1.6670 8.9750 -5.0000
-1.6670 6.3670 -5.0000 20.9000

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8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670
delpq =
0.2750
-0.3000

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0.2250
0.6500
vdel =
0.0575
0.0410

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0.0088
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Viva - voce
-0.0201

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VNEW =
1.0600 1.0575 1.0410
DELNEW =
0 0.0088 -0.0201
Result:

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Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of
small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.
Application:

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The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By
accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two
models with viscosity constant and variable across the oil film were developed.

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1. What is meant by jacobian matrix?
Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square
matrix, both the matrix
2. What are the different types of buses in power system network?
Slack bus, generator bus and load bus

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3. What are the information obtained from a load flow study?
The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each
bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.
4. What is the need for load flow study?

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Load flow studies determine if system voltages remain within specified limits under normal or emergency operating
conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are
commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?
P.Q,V,?

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6. Define - Voltage Controlled Bus
Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled
through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 15

(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 16

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2

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Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec

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Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.

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(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b

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4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY

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ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-

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Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1

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=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were

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analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?

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The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a

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power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging

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with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle

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The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?

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9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:

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To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6
Theory:

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Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1

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(k)
, PG 2
(k)
, ?PG N
(K)

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}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:

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Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.

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4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;

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warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;

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delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;

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while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));

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dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda

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p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:

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Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =

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8.5000
p =
400.0000
250.0000
150.0000

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Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2

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; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW

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100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc

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n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;

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for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;

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for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg

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for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))

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Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end
end

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Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)

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x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n

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x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n

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Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end
end
Pg

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Output:
lambda =
8.6149
Pg =
367.4040 379.4361 178.1598

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Pg =
350.0000 379.4361 178.1598
Demand new =
575
Lambda new =

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8.7147
Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were

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obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:
Used in power system with lowest cost and schedule with generating unit

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1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.

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3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint

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5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints

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7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:

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Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not

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included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:

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- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

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Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)

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For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.

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Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.

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2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve

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The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle

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Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-

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SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:

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MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and

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phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &

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steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;

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Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate

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sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));

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Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else
Q(i)= Q max(i)

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Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program

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Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run

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5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor

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values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

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Program:
clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')

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nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
PG=[0 .5 .4 .2];

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QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;
for i=1:nb

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Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;

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end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

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end
B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);

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end
c=V(p)*(A+B);
Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt

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Qg=Q*j;
Vt(p)=V(p);
else
if(Q<=Qmin)
Q=Qmin;

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else
Q=Qmax;
end
Vt(p)=1;
disp('it is load bus')

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Qg=Q*j
end
QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);

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end
B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end

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C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;

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for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))

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end
p=p+1;
end
Output:
Y bus =

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2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i

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Q =
0.1456, it is load bus
Q g =
0 + 0.1200i

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V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52



1. What is meant by load flow analysis?

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Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor

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3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators

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5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.

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Simplicity in technique
Small computer memory requirement
Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses

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9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD

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Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:
MATLAB 7.6
Theory:

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The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive

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power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.

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[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate

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P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max

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End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

Step 7: Change from specified Value
Declare dPa= Psp-P

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dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1

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Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses

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Step 13: Display the output
Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.

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Bus
Real load
demand, P D
Reactive Load
demand, Q D

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Real power
Generation, P G
Reactive Power
Generation, Q G
Voltage

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Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

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2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD
clc
clear all

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sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')

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Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i);
y(i)=(sa(i));

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Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end

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Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q
v=[1.06 1 1];

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

P=[0 0 0];
Q=[0 0 0];
del=[0 0 0];

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Pg=[0 0.2 0];
Pd=[0 0 0.6];
Qg=[0 0 0];
Qd=[0 0 0.25];
for p=2:nb

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for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);

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delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);
end
end
P;

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Q;
Pspe;
Qspe;
delP;
delQ;

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%Calculation of J1
P2=[0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb
if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));

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PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

end
end

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else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end

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PV;
% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
for j=1:nb
if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end

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end
else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end
end

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end
Pdel;
%Calculation of J3
Q2=[0 0 0];
for p=2:nb

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for q=2:nb
if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb
if (j~=p)

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Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 58

end

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end
else
QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));
end
end

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end
QV;
%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb
if(j~=p)

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Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end
end
else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
Qdel;
%Jacobian matrix

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PV(1,:)=[ ];
PV(:,1)=[ ];
Pdel(1,:)=[ ];
Pdel(:,1)=[ ];
QV(1,:)=[ ];

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QV(:,1)=[ ];
Qdel(1,:)=[ ];
Qdel(:,1)=[ ];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 59

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J=[PV Pdel;QV Qdel]
%Find the change in v&del
delP(1:1)=[];
delQ(1:1)=[];
delpq=[delP';delQ']

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vdel=inv(J)*delpq
%Find new v&del
for i=1:nb-1
for j=2:nb
vnew(i)=v(j)+vdel(i);

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delnew(i)=del(j)+vdel(i+2);
end
end
VNEW=[v(1) vnew]
DELNEW=[del(1) delnew

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Output:
Ybus =
6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i
-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i

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J =
2.8420 -1.6670 8.9750 -5.0000
-1.6670 6.3670 -5.0000 20.9000
8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670

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delpq =
0.2750
-0.3000
0.2250
0.6500

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vdel =
0.0575
0.0410
0.0088
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 60

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Viva - voce
-0.0201
VNEW =
1.0600 1.0575 1.0410

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DELNEW =
0 0.0088 -0.0201
Result:
Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of
small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.
Application:
The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By
accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two

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models with viscosity constant and variable across the oil film were developed.


1. What is meant by jacobian matrix?
Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square

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matrix, both the matrix
2. What are the different types of buses in power system network?
Slack bus, generator bus and load bus
3. What are the information obtained from a load flow study?
The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each

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bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.
4. What is the need for load flow study?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating
conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are

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commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?
P.Q,V,?
6. Define - Voltage Controlled Bus
Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled

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through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 61

The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular

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differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with
maximum real power.


8. What is meant by flat voltage start?

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The value of flat voltage start 1+j0
9. What are the advantages of Newton Raphson method?
Newton Raphson method needs less number of iterations to reach convergence, takes less
computation time
More accurate and not sensitive to the factors such like slack bus selection, regulation transformers

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etc. and the number of iterations required in this method is almost independent of system size.
10. What are the disadvantages of Newton Raphson method?
More calculations involved in each iteration and require large computation time per iteration and
large computer memory
Difficult solution technique (programming is difficult)

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FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

--- Content provided by FirstRanker.com ---

communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 13


1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 15

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y

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capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase

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per Kilometer of the line.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit

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%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;

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Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;

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a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);

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Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);

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Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);

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DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)

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L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving

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parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture

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when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next

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physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.

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This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?

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Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several

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advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.

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10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?

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In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:

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To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.

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Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium

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transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?

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Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?

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Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.

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6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND

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IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:

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MATLAB 7.6
Theory:
Formation of Y
bus
matrix:

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Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z

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bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.

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The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.

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Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)

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Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.

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(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus

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1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01

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2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04

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5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....
clc

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fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...

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r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...

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b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));

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end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m

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ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end
ybus = ybus % Bus Admittance Matrix

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zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:

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Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?

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Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view

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6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?

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Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm

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2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power

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system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.

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3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:

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Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady

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state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink

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Application:
To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?

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If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?

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In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?

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Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop

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Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power

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system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model

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3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9

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Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is

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computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the

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frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop

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Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:

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MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are

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marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.

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b) Verify the result using MATLAB program


Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)

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system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of

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operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.

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is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time

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The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time

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The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism

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8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.

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Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses

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Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:

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In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2

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(k)
, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which

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minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma

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Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1

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2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW

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C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.

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Program:
clc;
clear all;
warning off;
a=[.004; .006; .009];

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b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');

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fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;

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p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])

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lambda=lambda+dellambda;
end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda

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10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =

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400.0000
250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.

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Program:
clear
clc
n=3;
demand=925;

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a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
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c=[640 580 820];

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Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));

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y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));

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Pgtotal=sum(Pg);
end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));

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Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else

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Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);
end

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Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;

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for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));

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end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end

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end
end
Pg
Output:
lambda =

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8.6149
Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598

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Demand new =
575
Lambda new =
8.7147
Pg =

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350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:

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By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to

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meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to

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device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit

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Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch

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8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of

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system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

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To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.

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2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:

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1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.

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Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed

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- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:
For (a)

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Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;

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X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce

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Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)

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system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances

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3. Write the swing equation in a power system.

4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances

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5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:

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To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6
Theory:

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The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers

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were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]

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In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Get the input Value

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Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop

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For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)

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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)

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Q(i)<=Q min(i)
Else
Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);

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Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB

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2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:

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The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:
clc

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clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')

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sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i) ;

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y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);

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end
Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];

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Qmin=.05;
Qmax=.12;
for i=1:nb
Pg=PG(i);
Qg=QG(i);

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if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus

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for q=1:p-1
A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

end

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B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);

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Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);

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else
if(Q<=Qmin)
Q=Qmin;
else
Q=Qmax;

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end
Vt(p)=1;
disp('it is load bus')
Qg=Q*j
end

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QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);
end
B1=0;

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for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));

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elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

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A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));

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end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;

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end
Output:
Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i

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-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i


Q =

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0.1456, it is load bus
Q g =
0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i

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Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

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Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52

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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded

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2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,

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controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus

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6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement

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Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus

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10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method

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Software required:
MATLAB 7.6
Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are

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limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-

--- Content provided by FirstRanker.com ---

scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,

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some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6

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Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation

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Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max
End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

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Step 7: Change from specified Value
Declare dPa= Psp-P
dQa= Qsp- Q
dQ= Zeros(npq,1)

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Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with

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angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses
Step 13: Display the output
Step 14: End the Program

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Exercise:



Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

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1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus
Real load

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demand, P D
Reactive Load
demand, Q D
Real power
Generation, P G

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Reactive Power
Generation, Q G
Voltage
Specified
1 2 1 - - V 1=1.04

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2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

2. Verify the result using MATLAB
Program:

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%NEWTON RAPHSON METHOD
clc
clear all
sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')

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nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i);
y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
Ybusmag=abs(Ybus);

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Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q
v=[1.06 1 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

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P=[0 0 0];
Q=[0 0 0];
del=[0 0 0];
Pg=[0 0.2 0];
Pd=[0 0 0.6];

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Qg=[0 0 0];
Qd=[0 0 0.25];
for p=2:nb
for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));

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Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);
delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);

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end
end
P;
Q;
Pspe;

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Qspe;
delP;
delQ;

%Calculation of J1

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P2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));

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for j=1:nb
if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));
PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

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end
end
else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
PV;
% Calculation of J2

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Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb

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if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end
end
else

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Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end
end
end
Pdel;

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%Calculation of J3
Q2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)

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Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb
if (j~=p)
Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);

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end
end
else

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QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));
end
end

end

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QV;
%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
for j=1:nb
if(j~=p)
Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end

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end
else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end

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end
Qdel;
%Jacobian matrix
PV(1,:)=[ ];
PV(:,1)=[ ];

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Pdel(1,:)=[ ];
Pdel(:,1)=[ ];
QV(1,:)=[ ];
QV(:,1)=[ ];
Qdel(1,:)=[ ];

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Qdel(:,1)=[ ];
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J=[PV Pdel;QV Qdel]
%Find the change in v&del

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delP(1:1)=[];
delQ(1:1)=[];
delpq=[delP';delQ']
vdel=inv(J)*delpq
%Find new v&del

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for i=1:nb-1
for j=2:nb
vnew(i)=v(j)+vdel(i);
delnew(i)=del(j)+vdel(i+2);
end

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end
VNEW=[v(1) vnew]
DELNEW=[del(1) delnew
Output:
Ybus =

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6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i
-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i
J =
2.8420 -1.6670 8.9750 -5.0000

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-1.6670 6.3670 -5.0000 20.9000
8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670
delpq =
0.2750

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-0.3000
0.2250
0.6500
vdel =
0.0575

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0.0410
0.0088
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Viva - voce

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-0.0201
VNEW =
1.0600 1.0575 1.0410
DELNEW =
0 0.0088 -0.0201

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Result:
Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of
small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.

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Application:
The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By
accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two
models with viscosity constant and variable across the oil film were developed.

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1. What is meant by jacobian matrix?
Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square
matrix, both the matrix
2. What are the different types of buses in power system network?

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Slack bus, generator bus and load bus
3. What are the information obtained from a load flow study?
The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each
bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.

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4. What is the need for load flow study?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating
conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are
commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?

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P.Q,V,?
6. Define - Voltage Controlled Bus
Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled
through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?

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The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular
differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with
maximum real power.

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8. What is meant by flat voltage start?
The value of flat voltage start 1+j0
9. What are the advantages of Newton Raphson method?

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Newton Raphson method needs less number of iterations to reach convergence, takes less
computation time
More accurate and not sensitive to the factors such like slack bus selection, regulation transformers
etc. and the number of iterations required in this method is almost independent of system size.
10. What are the disadvantages of Newton Raphson method?

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More calculations involved in each iteration and require large computation time per iteration and
large computer memory
Difficult solution technique (programming is difficult)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 62

Expt.No.12: FAULT ANALYSIS IN POWER SYSTEM
Aim:
To become familiar with modeling and analysis of power systems under faulted condition and to compute the fault

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level, post-fault voltages and currents for different types of faults, both symmetric and unsymmetrical. To calculate
the fault current, post fault voltage and fault current through the branches for a three phase to ground fault in a small
power system and also study the effect of neighboring system. Check the results using available software. To obtain
the fault current, fault MVA, Post-fault bus voltages and fault current distribution for single line to ground fault, line-to-
line fault and double line to ground fault for a small power system, using the available software.To Carryout fault

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analysis for a sample power system for LLLG, LG, LL and LLG faults and prepare the report
Software required:
MATLAB 7.6
Theory:
Short circuit studies are performed to determine bus voltages and currents flowing in different parts the system

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when it is subjected to a fault. The current flowing immediately after the fault consists of an AC component which
eventually reaches steady state and a fast decaying DC component which decays to zero. Only the AC component is
considered in the analysis. The analysis is done using phasor technique assuming the system to be under quasi-
steady state and is done for various types of faults such as three-phase-to ground, line-to-ground, line-to-line and
double-line-to-ground. The results of fault studies are used to select the circuit breakers, set protective relays and to

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assess the voltage dips during fault. It is one of the primary studies to be performed whenever system expansion is
planned.
Modeling details:
Approximations:
The following approximations are usually made in fault analysis:

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1. Pre-fault load currents are neglected
2. Transformer taps are assumed to be nominal
3. A symmetric three phase power system is considered
4. Transmission line shunt capacitance and transformer magnetizing impedances are ignored
5. Series resistances of transmission lines are neglected

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6. The negative sequence impedance of alternators is assumed to be the same as their positive sequence
impedance
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

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communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y

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capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase

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per Kilometer of the line.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit

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%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;

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Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;

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a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);

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Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);

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Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);

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DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)

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L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving

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parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture

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when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next

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physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.

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This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?

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Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several

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advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.

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10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?

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In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:

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To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.

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Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium

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transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?

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Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?

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Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.

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6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND

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IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:

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MATLAB 7.6
Theory:
Formation of Y
bus
matrix:

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Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z

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bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.

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The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.

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Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)

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Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.

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(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus

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1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01

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2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04

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5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....
clc

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fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...

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r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...

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b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));

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end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m

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ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end
ybus = ybus % Bus Admittance Matrix

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zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:

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Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?

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Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view

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6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?

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Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm

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2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power

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system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.

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3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:

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Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady

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state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink

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Application:
To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?

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If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?

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In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?

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Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop

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Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power

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system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model

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3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9

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Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is

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computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the

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frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop

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Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:

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MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are

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marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.

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b) Verify the result using MATLAB program


Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)

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system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of

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operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.

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is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time

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The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time

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The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism

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8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.

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Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses

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Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:

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In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2

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(k)
, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which

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minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma

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Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1

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2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW

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C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.

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Program:
clc;
clear all;
warning off;
a=[.004; .006; .009];

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b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');

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fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;

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p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])

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lambda=lambda+dellambda;
end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda

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10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =

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400.0000
250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.

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Program:
clear
clc
n=3;
demand=925;

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a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];

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Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));

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y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));

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Pgtotal=sum(Pg);
end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));

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Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else

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Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);
end

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Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));

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end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end

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end
end
Pg
Output:
lambda =

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8.6149
Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598

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Demand new =
575
Lambda new =
8.7147
Pg =

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350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:

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By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to

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meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to

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device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit

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Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch

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8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of

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system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

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To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.

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2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:

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1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.

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Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed

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- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:
For (a)

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Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;

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X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce

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Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)

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system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances

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3. Write the swing equation in a power system.

4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances

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5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:

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To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6
Theory:

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The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers

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were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]

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In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Get the input Value

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Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop

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For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)

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Q(i)<=Q min(i)
Else
Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);

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Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB

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2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:

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The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:
clc

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clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')

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sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i) ;

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y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);

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end
Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];

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Qmin=.05;
Qmax=.12;
for i=1:nb
Pg=PG(i);
Qg=QG(i);

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if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus

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for q=1:p-1
A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

end

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B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);

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Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);

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else
if(Q<=Qmin)
Q=Qmin;
else
Q=Qmax;

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end
Vt(p)=1;
disp('it is load bus')
Qg=Q*j
end

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QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);
end
B1=0;

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for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));

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elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

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A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));

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end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;

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end
Output:
Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i

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-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i


Q =

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0.1456, it is load bus
Q g =
0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i

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Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

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Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52

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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded

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2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,

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controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus

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6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement

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Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus

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10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method

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Software required:
MATLAB 7.6
Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are

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limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-

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scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,

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some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6

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Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation

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Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max
End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

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Step 7: Change from specified Value
Declare dPa= Psp-P
dQa= Qsp- Q
dQ= Zeros(npq,1)

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Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with

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angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses
Step 13: Display the output
Step 14: End the Program

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Exercise:



Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

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1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus
Real load

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demand, P D
Reactive Load
demand, Q D
Real power
Generation, P G

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Reactive Power
Generation, Q G
Voltage
Specified
1 2 1 - - V 1=1.04

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2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

2. Verify the result using MATLAB
Program:

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%NEWTON RAPHSON METHOD
clc
clear all
sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')

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nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i);
y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
Ybusmag=abs(Ybus);

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Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q
v=[1.06 1 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

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P=[0 0 0];
Q=[0 0 0];
del=[0 0 0];
Pg=[0 0.2 0];
Pd=[0 0 0.6];

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Qg=[0 0 0];
Qd=[0 0 0.25];
for p=2:nb
for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));

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Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);
delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);

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end
end
P;
Q;
Pspe;

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Qspe;
delP;
delQ;

%Calculation of J1

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P2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));

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for j=1:nb
if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));
PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

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end
end
else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
PV;
% Calculation of J2

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Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb

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if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end
end
else

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Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end
end
end
Pdel;

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%Calculation of J3
Q2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)

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Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb
if (j~=p)
Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 58

end
end
else

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QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));
end
end

end

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QV;
%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
for j=1:nb
if(j~=p)
Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end

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end
else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end

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end
Qdel;
%Jacobian matrix
PV(1,:)=[ ];
PV(:,1)=[ ];

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Pdel(1,:)=[ ];
Pdel(:,1)=[ ];
QV(1,:)=[ ];
QV(:,1)=[ ];
Qdel(1,:)=[ ];

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Qdel(:,1)=[ ];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 59

J=[PV Pdel;QV Qdel]
%Find the change in v&del

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delP(1:1)=[];
delQ(1:1)=[];
delpq=[delP';delQ']
vdel=inv(J)*delpq
%Find new v&del

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for i=1:nb-1
for j=2:nb
vnew(i)=v(j)+vdel(i);
delnew(i)=del(j)+vdel(i+2);
end

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end
VNEW=[v(1) vnew]
DELNEW=[del(1) delnew
Output:
Ybus =

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6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i
-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i
J =
2.8420 -1.6670 8.9750 -5.0000

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-1.6670 6.3670 -5.0000 20.9000
8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670
delpq =
0.2750

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-0.3000
0.2250
0.6500
vdel =
0.0575

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0.0410
0.0088
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 60

Viva - voce

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-0.0201
VNEW =
1.0600 1.0575 1.0410
DELNEW =
0 0.0088 -0.0201

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Result:
Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of
small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.

--- Content provided by FirstRanker.com ---

Application:
The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By
accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two
models with viscosity constant and variable across the oil film were developed.

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1. What is meant by jacobian matrix?
Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square
matrix, both the matrix
2. What are the different types of buses in power system network?

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Slack bus, generator bus and load bus
3. What are the information obtained from a load flow study?
The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each
bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.

--- Content provided by FirstRanker.com ---

4. What is the need for load flow study?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating
conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are
commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?

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P.Q,V,?
6. Define - Voltage Controlled Bus
Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled
through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 61

The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular
differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with
maximum real power.

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8. What is meant by flat voltage start?
The value of flat voltage start 1+j0
9. What are the advantages of Newton Raphson method?

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Newton Raphson method needs less number of iterations to reach convergence, takes less
computation time
More accurate and not sensitive to the factors such like slack bus selection, regulation transformers
etc. and the number of iterations required in this method is almost independent of system size.
10. What are the disadvantages of Newton Raphson method?

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More calculations involved in each iteration and require large computation time per iteration and
large computer memory
Difficult solution technique (programming is difficult)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 62

Expt.No.12: FAULT ANALYSIS IN POWER SYSTEM
Aim:
To become familiar with modeling and analysis of power systems under faulted condition and to compute the fault

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level, post-fault voltages and currents for different types of faults, both symmetric and unsymmetrical. To calculate
the fault current, post fault voltage and fault current through the branches for a three phase to ground fault in a small
power system and also study the effect of neighboring system. Check the results using available software. To obtain
the fault current, fault MVA, Post-fault bus voltages and fault current distribution for single line to ground fault, line-to-
line fault and double line to ground fault for a small power system, using the available software.To Carryout fault

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analysis for a sample power system for LLLG, LG, LL and LLG faults and prepare the report
Software required:
MATLAB 7.6
Theory:
Short circuit studies are performed to determine bus voltages and currents flowing in different parts the system

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when it is subjected to a fault. The current flowing immediately after the fault consists of an AC component which
eventually reaches steady state and a fast decaying DC component which decays to zero. Only the AC component is
considered in the analysis. The analysis is done using phasor technique assuming the system to be under quasi-
steady state and is done for various types of faults such as three-phase-to ground, line-to-ground, line-to-line and
double-line-to-ground. The results of fault studies are used to select the circuit breakers, set protective relays and to

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assess the voltage dips during fault. It is one of the primary studies to be performed whenever system expansion is
planned.
Modeling details:
Approximations:
The following approximations are usually made in fault analysis:

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1. Pre-fault load currents are neglected
2. Transformer taps are assumed to be nominal
3. A symmetric three phase power system is considered
4. Transmission line shunt capacitance and transformer magnetizing impedances are ignored
5. Series resistances of transmission lines are neglected

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6. The negative sequence impedance of alternators is assumed to be the same as their positive sequence
impedance
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 63

In the case of symmetrical faults, it is sufficient to determine the currents and voltages in one phase. Hence the

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analysis is carried out on per phase basis (using + ve sequence Impedance network). In the case of unsymmetrical
faults, the method of symmetrical components is used.
Sequence impedances of power system components:
The sequence impedances of power system components namely generators, transmission lines and transformers
are required for modeling and analysis of unsymmetrical faults. In the case of overhead transmission lines the

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positive-and negative-sequence impedances are the same and the zero sequence impedance depends on ground
wire, tower footing resistance and grounding adopted.
In the case of transformers, the positive-and negative- sequence impedances are the same and the zero
sequence impedance depends on transformer winding connection, method of neutral grounding and transformer type
(shell or core).The positive-, negative-and zero-sequence impedances are different in the case of rotating equipment

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like synchronous generator, synchronous motor and induction motors. Estimation of sequence impedances of the
components and assembling of zero-, positive-and negative-sequence impedance networks are the major steps in
unsymmetrical fault analysis.
Short circuit computation:
Symmetrical fault analysis:

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Since the fault is symmetric the analysis is carried out on per phase basis. A short circuit represents a structural
change in the network which is equivalent to the addition of impedance (in the case of a symmetric short, three equal
impedances) at the location of fault. The changes in voltages and currents that result from this structural change can
be analyzed using Thevenin?s theorem which states: The changes that occur in the network voltages and currents
due to the addition of an impedance between two network nodes are identical with those voltages and currents that

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would be caused by an emf placed in series with the impedance and having a magnitude and polarity equal to the
pre-fault voltage that existed between the nodes in question and all other sources being zeroed. The post-fault
voltages and currents in the network are obtained by superposing these changes on the pre-fault voltages and
currents.
Example1:

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For the two-bus system shown in Fig .1, determine the fault current at the fault point and in other elements for a
fault at bus 2 with a fault impedance Z f . Load current can be assumed to be negligible. The pre-fault voltages at all
the buses can be assumed to be 1.0 p.u. The sub transient reactance of the generators and positive sequence
reactance of other elements are given. Assume that the resistances of all the elements are negligible.
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
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Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2

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Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec

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Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.

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(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b

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4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY

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ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-

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Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1

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=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were

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analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?

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The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a

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power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging

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with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle

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The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?

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9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:

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To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6
Theory:

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Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1

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(k)
, PG 2
(k)
, ?PG N
(K)

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}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:

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Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.

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4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;

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warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;

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delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;

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while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));

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dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda

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p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:

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Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =

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8.5000
p =
400.0000
250.0000
150.0000

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Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2

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; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW

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100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc

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n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;

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for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;

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for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg

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for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))

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Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end
end

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Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)

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x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n

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x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n

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Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end
end
Pg

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Output:
lambda =
8.6149
Pg =
367.4040 379.4361 178.1598

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Pg =
350.0000 379.4361 178.1598
Demand new =
575
Lambda new =

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8.7147
Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were

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obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:
Used in power system with lowest cost and schedule with generating unit

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1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.

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3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint

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5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints

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7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:

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Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not

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included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:

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- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

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Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)

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For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.

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Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.

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2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve

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The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle

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Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-

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SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:

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MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and

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phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &

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steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;

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Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate

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sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));

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Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else
Q(i)= Q max(i)

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Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program

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Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run

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5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor

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values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

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Program:
clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')

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nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
PG=[0 .5 .4 .2];

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QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;
for i=1:nb

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Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;

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end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

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end
B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);

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end
c=V(p)*(A+B);
Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt

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Qg=Q*j;
Vt(p)=V(p);
else
if(Q<=Qmin)
Q=Qmin;

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else
Q=Qmax;
end
Vt(p)=1;
disp('it is load bus')

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Qg=Q*j
end
QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);

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end
B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end

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C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;

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for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))

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end
p=p+1;
end
Output:
Y bus =

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2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i

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Q =
0.1456, it is load bus
Q g =
0 + 0.1200i

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V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52



1. What is meant by load flow analysis?

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Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor

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3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators

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5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.

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Simplicity in technique
Small computer memory requirement
Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses

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9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.

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Viva - voce
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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD

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Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:
MATLAB 7.6
Theory:

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The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive

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power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.

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[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate

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P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max

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End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

Step 7: Change from specified Value
Declare dPa= Psp-P

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dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1

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Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses

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Step 13: Display the output
Step 14: End the Program
Exercise:

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1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.

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Bus
Real load
demand, P D
Reactive Load
demand, Q D

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Real power
Generation, P G
Reactive Power
Generation, Q G
Voltage

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Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

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2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD
clc
clear all

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sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')

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Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i);
y(i)=(sa(i));

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Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end

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Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q
v=[1.06 1 1];

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P=[0 0 0];
Q=[0 0 0];
del=[0 0 0];

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Pg=[0 0.2 0];
Pd=[0 0 0.6];
Qg=[0 0 0];
Qd=[0 0 0.25];
for p=2:nb

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for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);

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delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);
end
end
P;

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Q;
Pspe;
Qspe;
delP;
delQ;

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%Calculation of J1
P2=[0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb
if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));

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PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

end
end

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else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end

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PV;
% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
for j=1:nb
if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end

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end
else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end
end

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end
Pdel;
%Calculation of J3
Q2=[0 0 0];
for p=2:nb

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for q=2:nb
if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb
if (j~=p)

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Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 58

end

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end
else
QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));
end
end

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end
QV;
%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb
if(j~=p)

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Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end
end
else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
Qdel;
%Jacobian matrix

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PV(1,:)=[ ];
PV(:,1)=[ ];
Pdel(1,:)=[ ];
Pdel(:,1)=[ ];
QV(1,:)=[ ];

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QV(:,1)=[ ];
Qdel(1,:)=[ ];
Qdel(:,1)=[ ];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 59

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J=[PV Pdel;QV Qdel]
%Find the change in v&del
delP(1:1)=[];
delQ(1:1)=[];
delpq=[delP';delQ']

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vdel=inv(J)*delpq
%Find new v&del
for i=1:nb-1
for j=2:nb
vnew(i)=v(j)+vdel(i);

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delnew(i)=del(j)+vdel(i+2);
end
end
VNEW=[v(1) vnew]
DELNEW=[del(1) delnew

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Output:
Ybus =
6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i
-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i

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J =
2.8420 -1.6670 8.9750 -5.0000
-1.6670 6.3670 -5.0000 20.9000
8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670

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delpq =
0.2750
-0.3000
0.2250
0.6500

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vdel =
0.0575
0.0410
0.0088
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 60

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Viva - voce
-0.0201
VNEW =
1.0600 1.0575 1.0410

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DELNEW =
0 0.0088 -0.0201
Result:
Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of
small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.
Application:
The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By
accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two

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models with viscosity constant and variable across the oil film were developed.


1. What is meant by jacobian matrix?
Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square

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matrix, both the matrix
2. What are the different types of buses in power system network?
Slack bus, generator bus and load bus
3. What are the information obtained from a load flow study?
The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each

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bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.
4. What is the need for load flow study?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating
conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are

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commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?
P.Q,V,?
6. Define - Voltage Controlled Bus
Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled

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through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 61

The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular

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differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with
maximum real power.


8. What is meant by flat voltage start?

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The value of flat voltage start 1+j0
9. What are the advantages of Newton Raphson method?
Newton Raphson method needs less number of iterations to reach convergence, takes less
computation time
More accurate and not sensitive to the factors such like slack bus selection, regulation transformers

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etc. and the number of iterations required in this method is almost independent of system size.
10. What are the disadvantages of Newton Raphson method?
More calculations involved in each iteration and require large computation time per iteration and
large computer memory
Difficult solution technique (programming is difficult)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 62

Expt.No.12: FAULT ANALYSIS IN POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of power systems under faulted condition and to compute the fault
level, post-fault voltages and currents for different types of faults, both symmetric and unsymmetrical. To calculate
the fault current, post fault voltage and fault current through the branches for a three phase to ground fault in a small
power system and also study the effect of neighboring system. Check the results using available software. To obtain

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the fault current, fault MVA, Post-fault bus voltages and fault current distribution for single line to ground fault, line-to-
line fault and double line to ground fault for a small power system, using the available software.To Carryout fault
analysis for a sample power system for LLLG, LG, LL and LLG faults and prepare the report
Software required:
MATLAB 7.6

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Theory:
Short circuit studies are performed to determine bus voltages and currents flowing in different parts the system
when it is subjected to a fault. The current flowing immediately after the fault consists of an AC component which
eventually reaches steady state and a fast decaying DC component which decays to zero. Only the AC component is
considered in the analysis. The analysis is done using phasor technique assuming the system to be under quasi-

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steady state and is done for various types of faults such as three-phase-to ground, line-to-ground, line-to-line and
double-line-to-ground. The results of fault studies are used to select the circuit breakers, set protective relays and to
assess the voltage dips during fault. It is one of the primary studies to be performed whenever system expansion is
planned.
Modeling details:

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Approximations:
The following approximations are usually made in fault analysis:
1. Pre-fault load currents are neglected
2. Transformer taps are assumed to be nominal
3. A symmetric three phase power system is considered

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4. Transmission line shunt capacitance and transformer magnetizing impedances are ignored
5. Series resistances of transmission lines are neglected
6. The negative sequence impedance of alternators is assumed to be the same as their positive sequence
impedance
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 63

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In the case of symmetrical faults, it is sufficient to determine the currents and voltages in one phase. Hence the
analysis is carried out on per phase basis (using + ve sequence Impedance network). In the case of unsymmetrical
faults, the method of symmetrical components is used.
Sequence impedances of power system components:

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The sequence impedances of power system components namely generators, transmission lines and transformers
are required for modeling and analysis of unsymmetrical faults. In the case of overhead transmission lines the
positive-and negative-sequence impedances are the same and the zero sequence impedance depends on ground
wire, tower footing resistance and grounding adopted.
In the case of transformers, the positive-and negative- sequence impedances are the same and the zero

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sequence impedance depends on transformer winding connection, method of neutral grounding and transformer type
(shell or core).The positive-, negative-and zero-sequence impedances are different in the case of rotating equipment
like synchronous generator, synchronous motor and induction motors. Estimation of sequence impedances of the
components and assembling of zero-, positive-and negative-sequence impedance networks are the major steps in
unsymmetrical fault analysis.

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Short circuit computation:
Symmetrical fault analysis:
Since the fault is symmetric the analysis is carried out on per phase basis. A short circuit represents a structural
change in the network which is equivalent to the addition of impedance (in the case of a symmetric short, three equal
impedances) at the location of fault. The changes in voltages and currents that result from this structural change can

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be analyzed using Thevenin?s theorem which states: The changes that occur in the network voltages and currents
due to the addition of an impedance between two network nodes are identical with those voltages and currents that
would be caused by an emf placed in series with the impedance and having a magnitude and polarity equal to the
pre-fault voltage that existed between the nodes in question and all other sources being zeroed. The post-fault
voltages and currents in the network are obtained by superposing these changes on the pre-fault voltages and

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currents.
Example1:
For the two-bus system shown in Fig .1, determine the fault current at the fault point and in other elements for a
fault at bus 2 with a fault impedance Z f . Load current can be assumed to be negligible. The pre-fault voltages at all
the buses can be assumed to be 1.0 p.u. The sub transient reactance of the generators and positive sequence

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reactance of other elements are given. Assume that the resistances of all the elements are negligible.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 64

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Fig 1 Symmetrical fault on a two bus system


First the ?Thevenin?s equivalent network? is formed Fig. 2a). The pre-fault voltage at bus2, V o2 equals 1.0 p.u. In
Fig 2a) the ?Thevenin?s emf? E th= V o2 = 1.0 is inserted in series with the short-circuit branch. The reduced Thevenin?s

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equivalent circuit is given in Fig 2c). In which the ?Thevenin?s equivalent impedance ?Z th is found to be j0.144p.u. It
should be noted that Z th is nothing but the driving point impedance at bus 2 which is the same as the diagonal
element Z 22 of bus impedance matrix of the network. With reference to Fig 2c). The fault current is given by

Fig. 2a)

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FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :

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Register No. :
Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and

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soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING

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To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and

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ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education

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2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables

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them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context

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5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)

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a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical

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and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large

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h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines

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2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System

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7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance

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matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.

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8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.

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11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.

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14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS

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Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19

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4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS

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8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58

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Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB

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Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:

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1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and

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communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development

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? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical

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manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:

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To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.

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Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file

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M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined

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function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.

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>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic

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equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.

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>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common

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data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.

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1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is

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>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;

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>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands

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and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];

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>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A

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Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];

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(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;

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Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:

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>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];

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>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.

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>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,

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element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.

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To explore these simply type
>>help if
>>help for
>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end

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- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);

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To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)

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>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.

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1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s

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usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;

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1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.

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To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)

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y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]

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>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available

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in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:

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Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping

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Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

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2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?

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For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi

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domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?

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poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?

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Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,

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12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application

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development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:

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Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of

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D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have

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a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:

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%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');

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r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);

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fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2

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A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various

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cases.
Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');

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H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);

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a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;

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c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);

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Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);

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DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;

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GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);

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DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km

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Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double

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circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?

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GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.

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4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?

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A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight

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and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?

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9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-

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section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load

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is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE

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PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).

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Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:

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Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?

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Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?

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The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?

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2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:

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Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element

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corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:

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In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can

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be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.

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Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)

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Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
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Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.

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5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02

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1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025

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3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')

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linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...

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b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...

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nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...

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for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....

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for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end

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end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus

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Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus

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admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27


1. What is meant by singular transformation method?
The matrix formed by graph theory.

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2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?

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Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.

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7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?

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Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.

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Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA

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POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:

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MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power

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supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.

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5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit

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The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2

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sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?

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Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load

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4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?

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frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM

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Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:

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MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.

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A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram

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5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

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Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA

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Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.

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(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and

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without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34


Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet

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the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?

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a and b
4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

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Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:

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To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:

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Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may

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come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small

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disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run

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5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d

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1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:

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By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact

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2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?

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The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability

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5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.

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7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more

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than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB

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Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6

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Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules

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{PG 1
(k)
, PG 2
(k)
, ?PG N

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(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.

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Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution

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Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File

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3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

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Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW

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C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2

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; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;

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clear all;
warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];

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Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])

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iter=0;
while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);

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J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end

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lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)

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Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0

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lambda =
8.5000
p =
400.0000
250.0000

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150.0000
Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1

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2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW

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C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW

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150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear

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clc
n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];

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x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y

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Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end

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Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else

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if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end

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end
Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand

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demandnew=demand-Pg(1)
x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

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for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1

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for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end
end

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Pg
Output:
lambda =
8.6149
Pg =

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367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598
Demand new =
575

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Lambda new =
8.7147
Pg =
350.0000 390.5242 184.4758
Result:

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Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:
Used in power system with lowest cost and schedule with generating unit

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1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?

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lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?

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Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?

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objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system

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9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)

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system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:

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I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds

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(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

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Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;

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eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained

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using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:

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Used to analysis to transient and steady state behavior of generator.



1. What is meant by steady state stability?

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power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

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4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

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6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

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Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm

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Software required:
MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best

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operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,

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computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,

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P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop

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if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else

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Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)

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Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window

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4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances

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are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

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Program:
clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')

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eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);

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for i=1:nl
k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);

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Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus

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PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;

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for i=1:nb
Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;

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Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

end
B=0;
for q=p:nb

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B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);
Q=-imag(c)

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if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);
else
if(Q<=Qmin)

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Q=Qmin;
else
Q=Qmax;
end
Vt(p)=1;

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disp('it is load bus')
Qg=Q*j
end
QG(p)=Qg;
for q=1:p-1

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A1=Ybus(p,q)*V(q);
end
B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));

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end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;

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for q=1:p-1
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

A2=A2-Ybus(p,q)*Vt(q);
end

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B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end
C2=(-PG(p)+(QG(p))/V(p));

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Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;
end
Output:

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Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i

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Q =
0.1456, it is load bus
Q g =

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0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power

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flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

Application:

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Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52

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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the

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acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus

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The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6

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7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement
Less computational time per iteration
8. List the advantages of load flow analysis.

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Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

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z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-

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RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:
MATLAB 7.6

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Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained

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from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit

--- Content provided by FirstRanker.com ---

fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.

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Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q

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Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2
Set for n=2: nbus

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Calculate Q(G), V(n) for Qmin or Q max
End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

Step 7: Change from specified Value

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Declare dPa= Psp-P
dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3
End the Loop

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Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]

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Step 12: Find line current flow & line Losses
Step 13: Display the output
Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total

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shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus
Real load
demand, P D
Reactive Load

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demand, Q D
Real power
Generation, P G
Reactive Power
Generation, Q G

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Voltage
Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

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2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD
clc

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clear all
sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')

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sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i);

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y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);

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end
Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q

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v=[1.06 1 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

P=[0 0 0];
Q=[0 0 0];

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del=[0 0 0];
Pg=[0 0.2 0];
Pd=[0 0 0.6];
Qg=[0 0 0];
Qd=[0 0 0.25];

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for p=2:nb
for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);

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Qspe(p)=Qg(p)-Qd(p);
delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);
end
end

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P;
Q;
Pspe;
Qspe;
delP;

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delQ;

%Calculation of J1
P2=[0 0 0];
for p=2:nb

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for q=2:nb
if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb
if (j~=p)

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P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));
PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

end

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end
else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end

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end
PV;
% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb

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for q=2:nb
if(p==q)
for j=1:nb
if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));

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end
end
else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end

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end
end
Pdel;
%Calculation of J3
Q2=[0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb

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if (j~=p)
Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 58

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end
end
else
QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));
end

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end

end
QV;
%Calculation of J4

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Qdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb

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if(j~=p)
Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end
end
else

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Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end
Qdel;

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%Jacobian matrix
PV(1,:)=[ ];
PV(:,1)=[ ];
Pdel(1,:)=[ ];
Pdel(:,1)=[ ];

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QV(1,:)=[ ];
QV(:,1)=[ ];
Qdel(1,:)=[ ];
Qdel(:,1)=[ ];
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J=[PV Pdel;QV Qdel]
%Find the change in v&del
delP(1:1)=[];
delQ(1:1)=[];

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delpq=[delP';delQ']
vdel=inv(J)*delpq
%Find new v&del
for i=1:nb-1
for j=2:nb

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vnew(i)=v(j)+vdel(i);
delnew(i)=del(j)+vdel(i+2);
end
end
VNEW=[v(1) vnew]

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DELNEW=[del(1) delnew
Output:
Ybus =
6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i
-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i

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-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i
J =
2.8420 -1.6670 8.9750 -5.0000
-1.6670 6.3670 -5.0000 20.9000
8.5250 -5.0000 -2.9920 1.6670

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-5.0000 19.1000 1.6670 -6.9670
delpq =
0.2750
-0.3000
0.2250

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0.6500
vdel =
0.0575
0.0410
0.0088

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Viva - voce
-0.0201
VNEW =

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1.0600 1.0575 1.0410
DELNEW =
0 0.0088 -0.0201
Result:
Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of

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small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.
Application:
The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By

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accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two
models with viscosity constant and variable across the oil film were developed.


1. What is meant by jacobian matrix?

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Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square
matrix, both the matrix
2. What are the different types of buses in power system network?
Slack bus, generator bus and load bus
3. What are the information obtained from a load flow study?

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The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each
bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.
4. What is the need for load flow study?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating

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conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are
commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?
P.Q,V,?
6. Define - Voltage Controlled Bus

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Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled
through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?
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The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular
differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with
maximum real power.

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8. What is meant by flat voltage start?
The value of flat voltage start 1+j0
9. What are the advantages of Newton Raphson method?
Newton Raphson method needs less number of iterations to reach convergence, takes less
computation time

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More accurate and not sensitive to the factors such like slack bus selection, regulation transformers
etc. and the number of iterations required in this method is almost independent of system size.
10. What are the disadvantages of Newton Raphson method?
More calculations involved in each iteration and require large computation time per iteration and
large computer memory

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Difficult solution technique (programming is difficult)


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Expt.No.12: FAULT ANALYSIS IN POWER SYSTEM
Aim:
To become familiar with modeling and analysis of power systems under faulted condition and to compute the fault
level, post-fault voltages and currents for different types of faults, both symmetric and unsymmetrical. To calculate
the fault current, post fault voltage and fault current through the branches for a three phase to ground fault in a small

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power system and also study the effect of neighboring system. Check the results using available software. To obtain
the fault current, fault MVA, Post-fault bus voltages and fault current distribution for single line to ground fault, line-to-
line fault and double line to ground fault for a small power system, using the available software.To Carryout fault
analysis for a sample power system for LLLG, LG, LL and LLG faults and prepare the report
Software required:

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MATLAB 7.6
Theory:
Short circuit studies are performed to determine bus voltages and currents flowing in different parts the system
when it is subjected to a fault. The current flowing immediately after the fault consists of an AC component which
eventually reaches steady state and a fast decaying DC component which decays to zero. Only the AC component is

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considered in the analysis. The analysis is done using phasor technique assuming the system to be under quasi-
steady state and is done for various types of faults such as three-phase-to ground, line-to-ground, line-to-line and
double-line-to-ground. The results of fault studies are used to select the circuit breakers, set protective relays and to
assess the voltage dips during fault. It is one of the primary studies to be performed whenever system expansion is
planned.

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Modeling details:
Approximations:
The following approximations are usually made in fault analysis:
1. Pre-fault load currents are neglected
2. Transformer taps are assumed to be nominal

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3. A symmetric three phase power system is considered
4. Transmission line shunt capacitance and transformer magnetizing impedances are ignored
5. Series resistances of transmission lines are neglected
6. The negative sequence impedance of alternators is assumed to be the same as their positive sequence
impedance

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In the case of symmetrical faults, it is sufficient to determine the currents and voltages in one phase. Hence the
analysis is carried out on per phase basis (using + ve sequence Impedance network). In the case of unsymmetrical
faults, the method of symmetrical components is used.

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Sequence impedances of power system components:
The sequence impedances of power system components namely generators, transmission lines and transformers
are required for modeling and analysis of unsymmetrical faults. In the case of overhead transmission lines the
positive-and negative-sequence impedances are the same and the zero sequence impedance depends on ground
wire, tower footing resistance and grounding adopted.

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In the case of transformers, the positive-and negative- sequence impedances are the same and the zero
sequence impedance depends on transformer winding connection, method of neutral grounding and transformer type
(shell or core).The positive-, negative-and zero-sequence impedances are different in the case of rotating equipment
like synchronous generator, synchronous motor and induction motors. Estimation of sequence impedances of the
components and assembling of zero-, positive-and negative-sequence impedance networks are the major steps in

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unsymmetrical fault analysis.
Short circuit computation:
Symmetrical fault analysis:
Since the fault is symmetric the analysis is carried out on per phase basis. A short circuit represents a structural
change in the network which is equivalent to the addition of impedance (in the case of a symmetric short, three equal

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impedances) at the location of fault. The changes in voltages and currents that result from this structural change can
be analyzed using Thevenin?s theorem which states: The changes that occur in the network voltages and currents
due to the addition of an impedance between two network nodes are identical with those voltages and currents that
would be caused by an emf placed in series with the impedance and having a magnitude and polarity equal to the
pre-fault voltage that existed between the nodes in question and all other sources being zeroed. The post-fault

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voltages and currents in the network are obtained by superposing these changes on the pre-fault voltages and
currents.
Example1:
For the two-bus system shown in Fig .1, determine the fault current at the fault point and in other elements for a
fault at bus 2 with a fault impedance Z f . Load current can be assumed to be negligible. The pre-fault voltages at all

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the buses can be assumed to be 1.0 p.u. The sub transient reactance of the generators and positive sequence
reactance of other elements are given. Assume that the resistances of all the elements are negligible.
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Fig 1 Symmetrical fault on a two bus system


First the ?Thevenin?s equivalent network? is formed Fig. 2a). The pre-fault voltage at bus2, V o2 equals 1.0 p.u. In

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Fig 2a) the ?Thevenin?s emf? E th= V o2 = 1.0 is inserted in series with the short-circuit branch. The reduced Thevenin?s
equivalent circuit is given in Fig 2c). In which the ?Thevenin?s equivalent impedance ?Z th is found to be j0.144p.u. It
should be noted that Z th is nothing but the driving point impedance at bus 2 which is the same as the diagonal
element Z 22 of bus impedance matrix of the network. With reference to Fig 2c). The fault current is given by

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Fig. 2a)
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Fig. 2b)

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Fig. 2c) Development of thevenin?s equivalent circuit (all impedances are in per unit)

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This current is the total fault current fed by both the generators. The contribution from each generator can be
computed by noting that the total current divides in inverse impedance ratio.
Interconnections with neighboring systems:
If a power system A, is interconnected to a neighboring system B, through, say a tie-line T 12, then for a fault at any

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of the buses in system A all the generators in system B also will feed the fault through the tie-line. Instead of
representing the complete network of the system B, the Thevenin?s equivalent circuit of system B can be connected
at the tie bus 2, (Fig 5.3).
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION

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VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in

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deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry

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? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION

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MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals

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To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and

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training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism

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To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,

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through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field

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b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems

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e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility

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i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.

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4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems

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9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.

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2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.

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6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi

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machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.

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12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS

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1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26

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6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41

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10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68

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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems

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Software required:
MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and

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programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.

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1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization

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? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small

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and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit

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(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,

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where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing

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them.
M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be

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called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace

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>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more

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generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the

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Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators

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2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)

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Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?

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>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in

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the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the

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workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence

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of commands
>>a=2;
>>b=5;
>>whos
>>clear all

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The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any

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DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is

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concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are

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considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,

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whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B

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Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)

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1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;

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>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];

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>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just

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>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if

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>>help for
>>help while
Example :

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]Looping :


>>if z=0
>>y=0

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>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:

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MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.

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>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)

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To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);

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The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The

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commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function

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We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.

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function y = admin(z)
y = 1./z
return

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Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,

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ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation

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Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:
MATLAB Used

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Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation

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Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield

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3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?

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If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.

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7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?

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An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application

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Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD

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GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');

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D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;

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x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);

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inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of

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1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:

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%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');

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dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;

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c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);

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Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);

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Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;

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Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)

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GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19



1. What is meant by geometric mean distance?

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GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?

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transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The

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high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.

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6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.

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Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such

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as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.

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11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor

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Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:

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Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.

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Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit

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3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?

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The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network

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Software required:
MATLAB 7.6
Theory:
Formation of Y
bus

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matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.

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Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful

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in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing

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buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:

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Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:

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(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03

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2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01

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4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....

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clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...

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tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...

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y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);

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ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch

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if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end

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ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using

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MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.

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3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?

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Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method

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8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?

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1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates

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the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:

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1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.

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(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce

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Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant

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3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.

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5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?

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Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:

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Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the

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governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:

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A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625

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damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec

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The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).

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Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?

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Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?

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Frequency control loop
Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS

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SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=

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0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both

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lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program


Result:

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Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37



1. What is meant by stability?

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Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively

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large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network

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4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.

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6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of

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synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.

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A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and

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without line losses
Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:

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Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)

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, PG 2
(k)
, ?PG N
(K)
}; k = 1,2,? .... N S

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Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program

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Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.

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5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;

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P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost

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in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;
warning off;

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a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;

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lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001

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iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;

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disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda
p

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10

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lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000

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p =
400.0000
250.0000
150.0000
Total cost = 6.6825e+003

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Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW

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C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2

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; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW

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Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc
n=3;

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demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n

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x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n

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Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg
for i=1:n

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if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);

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else
Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);

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end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;

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y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n
x1=x1+(b(i)/(2*a(i)));

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y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));

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end
end
end
Pg
Output:

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lambda =
8.6149
Pg =
367.4040 379.4361 178.1598
Pg =

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350.0000 379.4361 178.1598
Demand new =
575
Lambda new =
8.7147

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Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.

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Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch

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Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment

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Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.

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Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?

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Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI

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MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:

--- Content provided by FirstRanker.com ---

MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.

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(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1

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- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:

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For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)

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Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:

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By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?

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Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of

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variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD

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Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6

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Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power

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systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.

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[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;

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Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)

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Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop

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If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else
Q(i)= Q max(i)
Step 9: Check the condition for type

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V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:

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1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results

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Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using

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MATLAB.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:

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clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')

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nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);

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k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);

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Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];

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V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;
for i=1:nb
Pg=PG(i);

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Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;
end

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if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

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end
B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);
end

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c=V(p)*(A+B);
Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;

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Vt(p)=V(p);
else
if(Q<=Qmin)
Q=Qmin;
else

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Q=Qmax;
end
Vt(p)=1;
disp('it is load bus')
Qg=Q*j

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end
QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);
end

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B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));

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Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

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A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;
for q=p+1:nb

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B2=B2-(((Ybus(p,q))*V(q)));
end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))
end

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p=p+1;
end
Output:
Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0

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-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i

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Q =
0.1456, it is load bus
Q g =
0 + 0.1200i
V t =

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1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:

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By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52

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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,

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and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor
3. Define ? Slack Bus

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The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?

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Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.
Simplicity in technique

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Small computer memory requirement
Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?

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Load bus is P-Q bus
10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD
Aim:

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To determine the power flow analysis using Newton ? Raphson method
Software required:
MATLAB 7.6
Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear

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simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the

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power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]

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In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:
Step 1: Start the Program

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Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop

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Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max
End the Loop

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

Step 7: Change from specified Value
Declare dPa= Psp-P
dQa= Qsp- Q

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dQ= Zeros(npq,1)
Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3

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Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses
Step 13: Display the output

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Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus

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Real load
demand, P D
Reactive Load
demand, Q D
Real power

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Generation, P G
Reactive Power
Generation, Q G
Voltage
Specified

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1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

2. Verify the result using MATLAB

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Program:
%NEWTON RAPHSON METHOD
clc
clear all
sb=[1 1 2]; %input('Enter the starting bus = ')

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eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);

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for i=1:nl
k1=sb(i);
k2=eb(i);
y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);

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Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus

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Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q
v=[1.06 1 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

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P=[0 0 0];
Q=[0 0 0];
del=[0 0 0];
Pg=[0 0.2 0];

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Pd=[0 0 0.6];
Qg=[0 0 0];
Qd=[0 0 0.25];
for p=2:nb
for q=1:nb

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P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);
delP(p)=Pspe(p)-P(p);

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delQ(p)=Qspe(p)-Q(p);
end
end
P;
Q;

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Pspe;
Qspe;
delP;
delQ;

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%Calculation of J1
P2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)

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P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb
if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));
PV(p,q)=P1+P2(q);

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

end
end
else

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PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end
PV;

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% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb
if(p==q)

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for j=1:nb
if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end
end

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else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end
end
end

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Pdel;
%Calculation of J3
Q2=[0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb
if (j~=p)
Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));

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QV(p,q)=Q1+Q2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 58

end
end

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else
QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));
end
end

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end
QV;
%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb

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for q=2:nb
if(p==q)
for j=1:nb
if(j~=p)
Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));

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end
end
else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end

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end
end
Qdel;
%Jacobian matrix
PV(1,:)=[ ];

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PV(:,1)=[ ];
Pdel(1,:)=[ ];
Pdel(:,1)=[ ];
QV(1,:)=[ ];
QV(:,1)=[ ];

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Qdel(1,:)=[ ];
Qdel(:,1)=[ ];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 59

J=[PV Pdel;QV Qdel]

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%Find the change in v&del
delP(1:1)=[];
delQ(1:1)=[];
delpq=[delP';delQ']
vdel=inv(J)*delpq

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%Find new v&del
for i=1:nb-1
for j=2:nb
vnew(i)=v(j)+vdel(i);
delnew(i)=del(j)+vdel(i+2);

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end
end
VNEW=[v(1) vnew]
DELNEW=[del(1) delnew
Output:

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Ybus =
6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i
-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i
J =

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2.8420 -1.6670 8.9750 -5.0000
-1.6670 6.3670 -5.0000 20.9000
8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670
delpq =

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0.2750
-0.3000
0.2250
0.6500
vdel =

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0.0575
0.0410
0.0088
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 60

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Viva - voce
-0.0201
VNEW =
1.0600 1.0575 1.0410
DELNEW =

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0 0.0088 -0.0201
Result:
Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of
small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.
Outcome:

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By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.
Application:
The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By
accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two
models with viscosity constant and variable across the oil film were developed.

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1. What is meant by jacobian matrix?
Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square
matrix, both the matrix

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2. What are the different types of buses in power system network?
Slack bus, generator bus and load bus
3. What are the information obtained from a load flow study?
The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each
bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for

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hand solution of the power flow.
4. What is the need for load flow study?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating
conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are
commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles

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5. What are the quantities associated with each bus in a system?
P.Q,V,?
6. Define - Voltage Controlled Bus
Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled
through a prime mover while the terminal voltage is controlled through the generator excitation

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7. What is the need for slack bus?
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 61

The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular
differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with

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maximum real power.


8. What is meant by flat voltage start?
The value of flat voltage start 1+j0

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9. What are the advantages of Newton Raphson method?
Newton Raphson method needs less number of iterations to reach convergence, takes less
computation time
More accurate and not sensitive to the factors such like slack bus selection, regulation transformers
etc. and the number of iterations required in this method is almost independent of system size.

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10. What are the disadvantages of Newton Raphson method?
More calculations involved in each iteration and require large computation time per iteration and
large computer memory
Difficult solution technique (programming is difficult)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 62

Expt.No.12: FAULT ANALYSIS IN POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of power systems under faulted condition and to compute the fault
level, post-fault voltages and currents for different types of faults, both symmetric and unsymmetrical. To calculate
the fault current, post fault voltage and fault current through the branches for a three phase to ground fault in a small
power system and also study the effect of neighboring system. Check the results using available software. To obtain
the fault current, fault MVA, Post-fault bus voltages and fault current distribution for single line to ground fault, line-to-

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line fault and double line to ground fault for a small power system, using the available software.To Carryout fault
analysis for a sample power system for LLLG, LG, LL and LLG faults and prepare the report
Software required:
MATLAB 7.6
Theory:

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Short circuit studies are performed to determine bus voltages and currents flowing in different parts the system
when it is subjected to a fault. The current flowing immediately after the fault consists of an AC component which
eventually reaches steady state and a fast decaying DC component which decays to zero. Only the AC component is
considered in the analysis. The analysis is done using phasor technique assuming the system to be under quasi-
steady state and is done for various types of faults such as three-phase-to ground, line-to-ground, line-to-line and

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double-line-to-ground. The results of fault studies are used to select the circuit breakers, set protective relays and to
assess the voltage dips during fault. It is one of the primary studies to be performed whenever system expansion is
planned.
Modeling details:
Approximations:

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The following approximations are usually made in fault analysis:
1. Pre-fault load currents are neglected
2. Transformer taps are assumed to be nominal
3. A symmetric three phase power system is considered
4. Transmission line shunt capacitance and transformer magnetizing impedances are ignored

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5. Series resistances of transmission lines are neglected
6. The negative sequence impedance of alternators is assumed to be the same as their positive sequence
impedance
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In the case of symmetrical faults, it is sufficient to determine the currents and voltages in one phase. Hence the
analysis is carried out on per phase basis (using + ve sequence Impedance network). In the case of unsymmetrical
faults, the method of symmetrical components is used.
Sequence impedances of power system components:
The sequence impedances of power system components namely generators, transmission lines and transformers

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are required for modeling and analysis of unsymmetrical faults. In the case of overhead transmission lines the
positive-and negative-sequence impedances are the same and the zero sequence impedance depends on ground
wire, tower footing resistance and grounding adopted.
In the case of transformers, the positive-and negative- sequence impedances are the same and the zero
sequence impedance depends on transformer winding connection, method of neutral grounding and transformer type

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(shell or core).The positive-, negative-and zero-sequence impedances are different in the case of rotating equipment
like synchronous generator, synchronous motor and induction motors. Estimation of sequence impedances of the
components and assembling of zero-, positive-and negative-sequence impedance networks are the major steps in
unsymmetrical fault analysis.
Short circuit computation:

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Symmetrical fault analysis:
Since the fault is symmetric the analysis is carried out on per phase basis. A short circuit represents a structural
change in the network which is equivalent to the addition of impedance (in the case of a symmetric short, three equal
impedances) at the location of fault. The changes in voltages and currents that result from this structural change can
be analyzed using Thevenin?s theorem which states: The changes that occur in the network voltages and currents

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due to the addition of an impedance between two network nodes are identical with those voltages and currents that
would be caused by an emf placed in series with the impedance and having a magnitude and polarity equal to the
pre-fault voltage that existed between the nodes in question and all other sources being zeroed. The post-fault
voltages and currents in the network are obtained by superposing these changes on the pre-fault voltages and
currents.

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Example1:
For the two-bus system shown in Fig .1, determine the fault current at the fault point and in other elements for a
fault at bus 2 with a fault impedance Z f . Load current can be assumed to be negligible. The pre-fault voltages at all
the buses can be assumed to be 1.0 p.u. The sub transient reactance of the generators and positive sequence
reactance of other elements are given. Assume that the resistances of all the elements are negligible.

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Fig 1 Symmetrical fault on a two bus system

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First the ?Thevenin?s equivalent network? is formed Fig. 2a). The pre-fault voltage at bus2, V o2 equals 1.0 p.u. In
Fig 2a) the ?Thevenin?s emf? E th= V o2 = 1.0 is inserted in series with the short-circuit branch. The reduced Thevenin?s
equivalent circuit is given in Fig 2c). In which the ?Thevenin?s equivalent impedance ?Z th is found to be j0.144p.u. It

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should be noted that Z th is nothing but the driving point impedance at bus 2 which is the same as the diagonal
element Z 22 of bus impedance matrix of the network. With reference to Fig 2c). The fault current is given by

Fig. 2a)
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Fig. 2b)

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Fig. 2c) Development of thevenin?s equivalent circuit (all impedances are in per unit)


This current is the total fault current fed by both the generators. The contribution from each generator can be

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computed by noting that the total current divides in inverse impedance ratio.
Interconnections with neighboring systems:
If a power system A, is interconnected to a neighboring system B, through, say a tie-line T 12, then for a fault at any
of the buses in system A all the generators in system B also will feed the fault through the tie-line. Instead of
representing the complete network of the system B, the Thevenin?s equivalent circuit of system B can be connected

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at the tie bus 2, (Fig 5.3).
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The Thevenin?s equivalent reactance at bus 2 is given by
X Th, B = 1/SCC 2

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Where SCC 2 is the fault level of Bus2.
Thevenin?s source E Th, B may be assumed as 1.0 p.u

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Fig. 3 Thevenin?s equivalent for neighboring system
Systematic computation for large scale systems:

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The systematic computation procedure to be used for fault analysis of a large power systems using computer is
explained below. Let us consider a symmetric fault at bus r of an n-bus system. Let us assume that the pre-fault
currents are negligible.
Step: 1
Draw the pre-fault per phase network of the system (positive sequence network) (Fig 5.4).Obtain the positive

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sequence bus impedance matrix Z using Building Algorithm. All the machine reactance should be included in the Z
bus.

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Fig 4 Pre-fault per phase network (with loads neglected)
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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

LABORATORY MANUAL

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

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ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
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COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

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3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

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CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

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12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

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Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

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tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

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? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

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MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

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1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

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M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

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series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

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methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

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has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

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helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

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commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

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positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

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command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

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>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

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in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

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>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

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>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

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>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

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>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

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Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

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>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;

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>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);

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>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a

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pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some

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input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?

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z= [5 2 4;
1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;

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1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;

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1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2

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Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.

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Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics

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Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming

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in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations

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4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?

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Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i

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8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.

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10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?

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Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?

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Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and

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double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1

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A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 15

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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');

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d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))

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fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit
%3 phase double circuit

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S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');

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S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;

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b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);

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Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);

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Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);

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DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km

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C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:

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Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.

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2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines

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also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling

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5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically

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used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.

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8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?

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When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission

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line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.

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Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.

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Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load

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2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.

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4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?

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1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6

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Theory:
Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every

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transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus

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matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance

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matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:

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Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)

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Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.

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(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02

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1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02

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2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')

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fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...

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x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...

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nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end

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% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);

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end
end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix

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zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis

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Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27


1. What is meant by singular transformation method?

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The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.

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4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?

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loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance

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9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus

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11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.

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4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec

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Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with

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and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:

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To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple

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generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop

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7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the

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AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA

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POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram

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4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

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Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4

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Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in

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area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34


Application:

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To maintain the power and frequency constant in electrical power system.



1. What is meant by two area system?

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power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant

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3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop
Current control loop

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5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

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Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.

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(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:

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A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =

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0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.

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Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically

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the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system

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3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is

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the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its

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stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?

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The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The

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angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING

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MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:

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MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the

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total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2
(k)

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, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.

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This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda

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Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

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Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;

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P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:

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clc;
clear all;
warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];

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c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')

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disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);

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delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;

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end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000

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8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =
400.0000

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250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2

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; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:

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200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:

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clear
clc
n=3;
demand=925;
a=[.0056 .0045 .0079];

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b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];
Pmin=[200 250 125];

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Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));

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lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);

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end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);

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else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);

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end
end
Pgtotal=sum(Pg);
end
Pg

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if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

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for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end

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lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end

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end
Pg
Output:
lambda =
8.6149

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Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598
Demand new =

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575
Lambda new =
8.7147
Pg =
350.0000 390.5242 184.4758

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Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and

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without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:

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Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints

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2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints

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4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price

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6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?

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Minimum load Base load in power system
9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

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To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:
MATLAB 7.6
Theory:

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Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may

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come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small

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disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run

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5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system

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modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system

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for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.

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(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;

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X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;

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eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce
Result:

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Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming

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Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

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4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

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6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

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Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple

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method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow

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or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-

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scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to

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find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix

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Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0

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Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)

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Else
Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented

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Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.

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3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude

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at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:
clc
clear all

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sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')

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Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);

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Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end

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Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;

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Qmax=.12;
for i=1:nb
Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus

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p=1;
Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1

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A=Ybus(p,q)*V(q);
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end
B=0;

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for q=p:nb
B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);
Q=-imag(c)

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if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);
else

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if(Q<=Qmin)
Q=Qmin;
else
Q=Qmax;
end

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Vt(p)=1;
disp('it is load bus')
Qg=Q*j
end
QG(p)=Qg;

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for q=1:p-1
A1=Ybus(p,q)*V(q);
end
B1=0;
for q=p+1:nb

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B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus

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A2=0;
for q=1:p-1
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A2=A2-Ybus(p,q)*Vt(q);

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end
B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end

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C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;
end

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Output:
Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i

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0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i


Q =
0.1456, it is load bus

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Q g =
0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:

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Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

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Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52

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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?

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Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage

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4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?

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acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement
Less computational time per iteration

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8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

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z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:

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MATLAB 7.6
Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of

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power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical

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solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per

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kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max

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Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2

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Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max
End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

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Step 7: Change from specified Value
Declare dPa= Psp-P
dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3

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End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2

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Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses
Step 13: Display the output
Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

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1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus
Real load
demand, P D

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Reactive Load
demand, Q D
Real power
Generation, P G
Reactive Power

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Generation, Q G
Voltage
Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified

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3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD

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clc
clear all
sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')

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nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);

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k2=eb(i);
y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);

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Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);

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% Calculation of P and Q
v=[1.06 1 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

P=[0 0 0];

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Q=[0 0 0];
del=[0 0 0];
Pg=[0 0.2 0];
Pd=[0 0 0.6];
Qg=[0 0 0];

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Qd=[0 0 0.25];
for p=2:nb
for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));

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Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);
delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);
end

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end
P;
Q;
Pspe;
Qspe;

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delP;
delQ;

%Calculation of J1
P2=[0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb

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if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));
PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

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end
end
else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end

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end
end
PV;
% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb
if(j~=p)

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Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end
end
else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
Pdel;
%Calculation of J3

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Q2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));

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for j=1:nb
if (j~=p)
Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 58

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end
end
else
QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));

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end
end

end
QV;

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%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb
if(p==q)

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for j=1:nb
if(j~=p)
Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end
end

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else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end

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Qdel;
%Jacobian matrix
PV(1,:)=[ ];
PV(:,1)=[ ];
Pdel(1,:)=[ ];

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Pdel(:,1)=[ ];
QV(1,:)=[ ];
QV(:,1)=[ ];
Qdel(1,:)=[ ];
Qdel(:,1)=[ ];

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 59

J=[PV Pdel;QV Qdel]
%Find the change in v&del
delP(1:1)=[];

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delQ(1:1)=[];
delpq=[delP';delQ']
vdel=inv(J)*delpq
%Find new v&del
for i=1:nb-1

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for j=2:nb
vnew(i)=v(j)+vdel(i);
delnew(i)=del(j)+vdel(i+2);
end
end

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VNEW=[v(1) vnew]
DELNEW=[del(1) delnew
Output:
Ybus =
6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i

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-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i
J =
2.8420 -1.6670 8.9750 -5.0000
-1.6670 6.3670 -5.0000 20.9000

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8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670
delpq =
0.2750
-0.3000

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0.2250
0.6500
vdel =
0.0575
0.0410

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0.0088
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 60

Viva - voce
-0.0201

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VNEW =
1.0600 1.0575 1.0410
DELNEW =
0 0.0088 -0.0201
Result:

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Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of
small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.
Application:

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The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By
accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two
models with viscosity constant and variable across the oil film were developed.

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1. What is meant by jacobian matrix?
Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square
matrix, both the matrix
2. What are the different types of buses in power system network?
Slack bus, generator bus and load bus

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3. What are the information obtained from a load flow study?
The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each
bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.
4. What is the need for load flow study?

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Load flow studies determine if system voltages remain within specified limits under normal or emergency operating
conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are
commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?
P.Q,V,?

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6. Define - Voltage Controlled Bus
Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled
through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 61

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The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular
differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with
maximum real power.

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8. What is meant by flat voltage start?
The value of flat voltage start 1+j0
9. What are the advantages of Newton Raphson method?
Newton Raphson method needs less number of iterations to reach convergence, takes less

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computation time
More accurate and not sensitive to the factors such like slack bus selection, regulation transformers
etc. and the number of iterations required in this method is almost independent of system size.
10. What are the disadvantages of Newton Raphson method?
More calculations involved in each iteration and require large computation time per iteration and

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large computer memory
Difficult solution technique (programming is difficult)


Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 62

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Expt.No.12: FAULT ANALYSIS IN POWER SYSTEM
Aim:
To become familiar with modeling and analysis of power systems under faulted condition and to compute the fault
level, post-fault voltages and currents for different types of faults, both symmetric and unsymmetrical. To calculate

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the fault current, post fault voltage and fault current through the branches for a three phase to ground fault in a small
power system and also study the effect of neighboring system. Check the results using available software. To obtain
the fault current, fault MVA, Post-fault bus voltages and fault current distribution for single line to ground fault, line-to-
line fault and double line to ground fault for a small power system, using the available software.To Carryout fault
analysis for a sample power system for LLLG, LG, LL and LLG faults and prepare the report

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Software required:
MATLAB 7.6
Theory:
Short circuit studies are performed to determine bus voltages and currents flowing in different parts the system
when it is subjected to a fault. The current flowing immediately after the fault consists of an AC component which

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eventually reaches steady state and a fast decaying DC component which decays to zero. Only the AC component is
considered in the analysis. The analysis is done using phasor technique assuming the system to be under quasi-
steady state and is done for various types of faults such as three-phase-to ground, line-to-ground, line-to-line and
double-line-to-ground. The results of fault studies are used to select the circuit breakers, set protective relays and to
assess the voltage dips during fault. It is one of the primary studies to be performed whenever system expansion is

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planned.
Modeling details:
Approximations:
The following approximations are usually made in fault analysis:
1. Pre-fault load currents are neglected

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2. Transformer taps are assumed to be nominal
3. A symmetric three phase power system is considered
4. Transmission line shunt capacitance and transformer magnetizing impedances are ignored
5. Series resistances of transmission lines are neglected
6. The negative sequence impedance of alternators is assumed to be the same as their positive sequence

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impedance
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In the case of symmetrical faults, it is sufficient to determine the currents and voltages in one phase. Hence the
analysis is carried out on per phase basis (using + ve sequence Impedance network). In the case of unsymmetrical

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faults, the method of symmetrical components is used.
Sequence impedances of power system components:
The sequence impedances of power system components namely generators, transmission lines and transformers
are required for modeling and analysis of unsymmetrical faults. In the case of overhead transmission lines the
positive-and negative-sequence impedances are the same and the zero sequence impedance depends on ground

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wire, tower footing resistance and grounding adopted.
In the case of transformers, the positive-and negative- sequence impedances are the same and the zero
sequence impedance depends on transformer winding connection, method of neutral grounding and transformer type
(shell or core).The positive-, negative-and zero-sequence impedances are different in the case of rotating equipment
like synchronous generator, synchronous motor and induction motors. Estimation of sequence impedances of the

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components and assembling of zero-, positive-and negative-sequence impedance networks are the major steps in
unsymmetrical fault analysis.
Short circuit computation:
Symmetrical fault analysis:
Since the fault is symmetric the analysis is carried out on per phase basis. A short circuit represents a structural

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change in the network which is equivalent to the addition of impedance (in the case of a symmetric short, three equal
impedances) at the location of fault. The changes in voltages and currents that result from this structural change can
be analyzed using Thevenin?s theorem which states: The changes that occur in the network voltages and currents
due to the addition of an impedance between two network nodes are identical with those voltages and currents that
would be caused by an emf placed in series with the impedance and having a magnitude and polarity equal to the

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pre-fault voltage that existed between the nodes in question and all other sources being zeroed. The post-fault
voltages and currents in the network are obtained by superposing these changes on the pre-fault voltages and
currents.
Example1:
For the two-bus system shown in Fig .1, determine the fault current at the fault point and in other elements for a

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fault at bus 2 with a fault impedance Z f . Load current can be assumed to be negligible. The pre-fault voltages at all
the buses can be assumed to be 1.0 p.u. The sub transient reactance of the generators and positive sequence
reactance of other elements are given. Assume that the resistances of all the elements are negligible.
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Fig 1 Symmetrical fault on a two bus system

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First the ?Thevenin?s equivalent network? is formed Fig. 2a). The pre-fault voltage at bus2, V o2 equals 1.0 p.u. In
Fig 2a) the ?Thevenin?s emf? E th= V o2 = 1.0 is inserted in series with the short-circuit branch. The reduced Thevenin?s
equivalent circuit is given in Fig 2c). In which the ?Thevenin?s equivalent impedance ?Z th is found to be j0.144p.u. It
should be noted that Z th is nothing but the driving point impedance at bus 2 which is the same as the diagonal
element Z 22 of bus impedance matrix of the network. With reference to Fig 2c). The fault current is given by

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Fig. 2a)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 65

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Fig. 2b)

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Fig. 2c) Development of thevenin?s equivalent circuit (all impedances are in per unit)

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This current is the total fault current fed by both the generators. The contribution from each generator can be
computed by noting that the total current divides in inverse impedance ratio.
Interconnections with neighboring systems:

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If a power system A, is interconnected to a neighboring system B, through, say a tie-line T 12, then for a fault at any
of the buses in system A all the generators in system B also will feed the fault through the tie-line. Instead of
representing the complete network of the system B, the Thevenin?s equivalent circuit of system B can be connected
at the tie bus 2, (Fig 5.3).
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 66

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The Thevenin?s equivalent reactance at bus 2 is given by
X Th, B = 1/SCC 2
Where SCC 2 is the fault level of Bus2.
Thevenin?s source E Th, B may be assumed as 1.0 p.u

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Fig. 3 Thevenin?s equivalent for neighboring system
Systematic computation for large scale systems:
The systematic computation procedure to be used for fault analysis of a large power systems using computer is
explained below. Let us consider a symmetric fault at bus r of an n-bus system. Let us assume that the pre-fault

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currents are negligible.
Step: 1
Draw the pre-fault per phase network of the system (positive sequence network) (Fig 5.4).Obtain the positive
sequence bus impedance matrix Z using Building Algorithm. All the machine reactance should be included in the Z
bus.

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Fig 4 Pre-fault per phase network (with loads neglected)
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Viva - voce
Step: 2
Obtain the falut current using the Thevenin?s equivalent of the system feeding the foult as explained below.
Assume fault impedance as Z

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f
. TH=he thevenin?s eqivalent of the system feeding the faulf impedance is given in
figure 5.5.

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Step: 3
Fig.5 Thevenin?s Equivalent of the system feeding the fault
Obtain the Thevenin?s Equivalent network
Result:

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Thus, the modeling and analysis of power systems under faulted condition and to compute the fault level, post-fault
voltages and currents for different types of faults were obtained using MATLAB.
Outcome:
By doing the experiment, the fault analysis in power system has been done using MATLAB and different types of
faults have been solved using MATLAB.

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Application:
Short Circuit Analysis is performed to determine the currents that flow in a power system under fault
conditions.A Short Circuit Analysis will help to ensure that personnel and equipment are protected by
establishing proper interrupting ratings of protective devices

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1. What is meant by fault?
In an electric power system, a fault or fault current is any abnormal electric current. For example, a short circuit is a fault in
which current bypasses the normal load.
2. What are the different types of fault?

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LG, LL ,LLG and symmetrical fault

FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

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LABORATORY MANUAL
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VISION
VISION

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is committed to provide highly disciplined, conscientious and

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enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in

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communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,

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enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions

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3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the

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students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints

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such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks

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f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities

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j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES

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COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.

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LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.

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5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems

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10. Economic Dispatch in Power Systems.


1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.

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3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.

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7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.

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10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.

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13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05

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2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29

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7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44

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11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:

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MATLAB
Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical

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notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:

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? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics

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? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering

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applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)

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>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.

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M-files can be classified into following 2 categories,


i) Script M-files ? Main file contains commands and from which functions can also be
called

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ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus

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These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will

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be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model

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of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions

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3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in

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the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt

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(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.

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/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should

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always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands

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>>a=2;
>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5

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respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.

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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

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>>a=4.2:
>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.

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>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB

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prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0

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seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:

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Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all
>> a=4;
>> A=7;

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>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];

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>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]

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1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for

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>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else

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>>y=1/z
>>end


>>for n=1:2:10

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>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of

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commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all

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>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use

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>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level

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approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the

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new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of

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given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,

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>>z=[5 2 4;
1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25

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1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then

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build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power

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systems problems.

Application:
MATLAB Used
Algorithm development

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Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?

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MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?

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Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else

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6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?

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ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads

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the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.

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11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.

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13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

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To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:

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Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)

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1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');

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D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;

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Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y

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capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km

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The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase

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per Kilometer of the line.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,

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C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit

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%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;

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Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;

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a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);

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Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);

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Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 18

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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);

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DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)

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L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving

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parameters of transmission lines.

Application :
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture

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when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next

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physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.

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This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?

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Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several

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advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.

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10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?

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In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:

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To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.

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Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.

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5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium

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transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?

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Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?

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Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.

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6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

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The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND

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IMPEDANCE MATRICES

Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:

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MATLAB 7.6
Theory:
Formation of Y
bus
matrix:

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Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z

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bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.

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The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.

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Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)

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Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.

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(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus

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1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01

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2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04

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5 6 0.10 0.30 0.03

Program:
% Program to form Admittance and Impedance Bus Formation....
clc

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fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...

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r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...

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b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));

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end
% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m

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ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end
end
ybus = ybus % Bus Admittance Matrix

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zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:

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Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?

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Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view

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6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?

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Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm

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2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

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The manufacture is used as common value

It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power

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system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.

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3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:

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Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady

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state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:

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Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink

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Application:
To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?

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If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?

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In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?

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Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop

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Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

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AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

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Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power

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system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system

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to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the

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change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model

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3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9

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Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is

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computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow

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dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the

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frequency constant
3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop

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Current control loop
5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:

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MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are

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steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.

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Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,

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(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

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Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are

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marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.

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b) Verify the result using MATLAB program


Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)

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system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of

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operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.

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is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time

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The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time

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The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism

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8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.

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Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

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Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses

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Software required:
MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:

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In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2

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(k)
, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which

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minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma

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Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1

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2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW

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C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.

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Program:
clc;
clear all;
warning off;
a=[.004; .006; .009];

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b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');

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fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;

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p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])

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lambda=lambda+dellambda;
end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda

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10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =

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400.0000
250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.

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Program:
clear
clc
n=3;
demand=925;

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a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];

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Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));

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y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));

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Pgtotal=sum(Pg);
end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));

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Pg(i);
else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else

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Pg(i)=Pmax(i);
end
end
Pgtotal=sum(Pg);
end

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Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));

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end
lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end

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end
end
Pg
Output:
lambda =

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8.6149
Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598

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Demand new =
575
Lambda new =
8.7147
Pg =

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350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:

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By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

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Application:
Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to

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meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to

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device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit

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Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch

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8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of

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system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

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To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.

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2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:

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1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.

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Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed

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- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:
For (a)

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Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;

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X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce

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Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)

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system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances

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3. Write the swing equation in a power system.

4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances

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5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:

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To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6
Theory:

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The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers

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were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]

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In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Get the input Value

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Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop

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For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)

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Q(i)<=Q min(i)
Else
Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);

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Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB

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2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:

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The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:
clc

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clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')

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sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i) ;

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y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);

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end
Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];

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Qmin=.05;
Qmax=.12;
for i=1:nb
Pg=PG(i);
Qg=QG(i);

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if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus

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for q=1:p-1
A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

end

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B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);

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Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);

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else
if(Q<=Qmin)
Q=Qmin;
else
Q=Qmax;

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end
Vt(p)=1;
disp('it is load bus')
Qg=Q*j
end

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QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);
end
B1=0;

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for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));

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elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

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A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));

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end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;

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end
Output:
Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i

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-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i


Q =

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0.1456, it is load bus
Q g =
0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i

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Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

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Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52

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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded

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2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,

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controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus

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6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement

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Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus

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10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method

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Software required:
MATLAB 7.6
Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are

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limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-

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scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,

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some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6

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Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation

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Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max
End the Loop
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Step 7: Change from specified Value
Declare dPa= Psp-P
dQa= Qsp- Q
dQ= Zeros(npq,1)

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Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with

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angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses
Step 13: Display the output
Step 14: End the Program

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Exercise:



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1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus
Real load

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demand, P D
Reactive Load
demand, Q D
Real power
Generation, P G

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Reactive Power
Generation, Q G
Voltage
Specified
1 2 1 - - V 1=1.04

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2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

2. Verify the result using MATLAB
Program:

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%NEWTON RAPHSON METHOD
clc
clear all
sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')

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nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i);
y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
Ybusmag=abs(Ybus);

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Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q
v=[1.06 1 1];
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P=[0 0 0];
Q=[0 0 0];
del=[0 0 0];
Pg=[0 0.2 0];
Pd=[0 0 0.6];

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Qg=[0 0 0];
Qd=[0 0 0.25];
for p=2:nb
for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));

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Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);
delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);

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end
end
P;
Q;
Pspe;

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Qspe;
delP;
delQ;

%Calculation of J1

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P2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));

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for j=1:nb
if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));
PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

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end
end
else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
PV;
% Calculation of J2

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Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb

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if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end
end
else

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Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end
end
end
Pdel;

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%Calculation of J3
Q2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)

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Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb
if (j~=p)
Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);

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end
end
else

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QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));
end
end

end

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QV;
%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
for j=1:nb
if(j~=p)
Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end

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end
else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end

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end
Qdel;
%Jacobian matrix
PV(1,:)=[ ];
PV(:,1)=[ ];

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Pdel(1,:)=[ ];
Pdel(:,1)=[ ];
QV(1,:)=[ ];
QV(:,1)=[ ];
Qdel(1,:)=[ ];

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Qdel(:,1)=[ ];
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J=[PV Pdel;QV Qdel]
%Find the change in v&del

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delP(1:1)=[];
delQ(1:1)=[];
delpq=[delP';delQ']
vdel=inv(J)*delpq
%Find new v&del

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for i=1:nb-1
for j=2:nb
vnew(i)=v(j)+vdel(i);
delnew(i)=del(j)+vdel(i+2);
end

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end
VNEW=[v(1) vnew]
DELNEW=[del(1) delnew
Output:
Ybus =

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6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i
-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i
J =
2.8420 -1.6670 8.9750 -5.0000

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-1.6670 6.3670 -5.0000 20.9000
8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670
delpq =
0.2750

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-0.3000
0.2250
0.6500
vdel =
0.0575

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0.0410
0.0088
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Viva - voce

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-0.0201
VNEW =
1.0600 1.0575 1.0410
DELNEW =
0 0.0088 -0.0201

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Result:
Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of
small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.

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Application:
The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By
accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two
models with viscosity constant and variable across the oil film were developed.

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1. What is meant by jacobian matrix?
Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square
matrix, both the matrix
2. What are the different types of buses in power system network?

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Slack bus, generator bus and load bus
3. What are the information obtained from a load flow study?
The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each
bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.

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4. What is the need for load flow study?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating
conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are
commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?

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P.Q,V,?
6. Define - Voltage Controlled Bus
Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled
through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?

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The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular
differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with
maximum real power.

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8. What is meant by flat voltage start?
The value of flat voltage start 1+j0
9. What are the advantages of Newton Raphson method?

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Newton Raphson method needs less number of iterations to reach convergence, takes less
computation time
More accurate and not sensitive to the factors such like slack bus selection, regulation transformers
etc. and the number of iterations required in this method is almost independent of system size.
10. What are the disadvantages of Newton Raphson method?

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More calculations involved in each iteration and require large computation time per iteration and
large computer memory
Difficult solution technique (programming is difficult)

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Expt.No.12: FAULT ANALYSIS IN POWER SYSTEM
Aim:
To become familiar with modeling and analysis of power systems under faulted condition and to compute the fault

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level, post-fault voltages and currents for different types of faults, both symmetric and unsymmetrical. To calculate
the fault current, post fault voltage and fault current through the branches for a three phase to ground fault in a small
power system and also study the effect of neighboring system. Check the results using available software. To obtain
the fault current, fault MVA, Post-fault bus voltages and fault current distribution for single line to ground fault, line-to-
line fault and double line to ground fault for a small power system, using the available software.To Carryout fault

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analysis for a sample power system for LLLG, LG, LL and LLG faults and prepare the report
Software required:
MATLAB 7.6
Theory:
Short circuit studies are performed to determine bus voltages and currents flowing in different parts the system

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when it is subjected to a fault. The current flowing immediately after the fault consists of an AC component which
eventually reaches steady state and a fast decaying DC component which decays to zero. Only the AC component is
considered in the analysis. The analysis is done using phasor technique assuming the system to be under quasi-
steady state and is done for various types of faults such as three-phase-to ground, line-to-ground, line-to-line and
double-line-to-ground. The results of fault studies are used to select the circuit breakers, set protective relays and to

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assess the voltage dips during fault. It is one of the primary studies to be performed whenever system expansion is
planned.
Modeling details:
Approximations:
The following approximations are usually made in fault analysis:

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1. Pre-fault load currents are neglected
2. Transformer taps are assumed to be nominal
3. A symmetric three phase power system is considered
4. Transmission line shunt capacitance and transformer magnetizing impedances are ignored
5. Series resistances of transmission lines are neglected

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6. The negative sequence impedance of alternators is assumed to be the same as their positive sequence
impedance
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In the case of symmetrical faults, it is sufficient to determine the currents and voltages in one phase. Hence the

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analysis is carried out on per phase basis (using + ve sequence Impedance network). In the case of unsymmetrical
faults, the method of symmetrical components is used.
Sequence impedances of power system components:
The sequence impedances of power system components namely generators, transmission lines and transformers
are required for modeling and analysis of unsymmetrical faults. In the case of overhead transmission lines the

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positive-and negative-sequence impedances are the same and the zero sequence impedance depends on ground
wire, tower footing resistance and grounding adopted.
In the case of transformers, the positive-and negative- sequence impedances are the same and the zero
sequence impedance depends on transformer winding connection, method of neutral grounding and transformer type
(shell or core).The positive-, negative-and zero-sequence impedances are different in the case of rotating equipment

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like synchronous generator, synchronous motor and induction motors. Estimation of sequence impedances of the
components and assembling of zero-, positive-and negative-sequence impedance networks are the major steps in
unsymmetrical fault analysis.
Short circuit computation:
Symmetrical fault analysis:

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Since the fault is symmetric the analysis is carried out on per phase basis. A short circuit represents a structural
change in the network which is equivalent to the addition of impedance (in the case of a symmetric short, three equal
impedances) at the location of fault. The changes in voltages and currents that result from this structural change can
be analyzed using Thevenin?s theorem which states: The changes that occur in the network voltages and currents
due to the addition of an impedance between two network nodes are identical with those voltages and currents that

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would be caused by an emf placed in series with the impedance and having a magnitude and polarity equal to the
pre-fault voltage that existed between the nodes in question and all other sources being zeroed. The post-fault
voltages and currents in the network are obtained by superposing these changes on the pre-fault voltages and
currents.
Example1:

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For the two-bus system shown in Fig .1, determine the fault current at the fault point and in other elements for a
fault at bus 2 with a fault impedance Z f . Load current can be assumed to be negligible. The pre-fault voltages at all
the buses can be assumed to be 1.0 p.u. The sub transient reactance of the generators and positive sequence
reactance of other elements are given. Assume that the resistances of all the elements are negligible.
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Fig 1 Symmetrical fault on a two bus system

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First the ?Thevenin?s equivalent network? is formed Fig. 2a). The pre-fault voltage at bus2, V o2 equals 1.0 p.u. In
Fig 2a) the ?Thevenin?s emf? E th= V o2 = 1.0 is inserted in series with the short-circuit branch. The reduced Thevenin?s
equivalent circuit is given in Fig 2c). In which the ?Thevenin?s equivalent impedance ?Z th is found to be j0.144p.u. It
should be noted that Z th is nothing but the driving point impedance at bus 2 which is the same as the diagonal

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element Z 22 of bus impedance matrix of the network. With reference to Fig 2c). The fault current is given by

Fig. 2a)
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Fig. 2b)

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Fig. 2c) Development of thevenin?s equivalent circuit (all impedances are in per unit)


This current is the total fault current fed by both the generators. The contribution from each generator can be
computed by noting that the total current divides in inverse impedance ratio.

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Interconnections with neighboring systems:
If a power system A, is interconnected to a neighboring system B, through, say a tie-line T 12, then for a fault at any
of the buses in system A all the generators in system B also will feed the fault through the tie-line. Instead of
representing the complete network of the system B, the Thevenin?s equivalent circuit of system B can be connected
at the tie bus 2, (Fig 5.3).

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 66

The Thevenin?s equivalent reactance at bus 2 is given by
X Th, B = 1/SCC 2
Where SCC 2 is the fault level of Bus2.

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Thevenin?s source E Th, B may be assumed as 1.0 p.u

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Fig. 3 Thevenin?s equivalent for neighboring system
Systematic computation for large scale systems:
The systematic computation procedure to be used for fault analysis of a large power systems using computer is

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explained below. Let us consider a symmetric fault at bus r of an n-bus system. Let us assume that the pre-fault
currents are negligible.
Step: 1
Draw the pre-fault per phase network of the system (positive sequence network) (Fig 5.4).Obtain the positive
sequence bus impedance matrix Z using Building Algorithm. All the machine reactance should be included in the Z

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bus.



Fig 4 Pre-fault per phase network (with loads neglected)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 67

Viva - voce
Step: 2
Obtain the falut current using the Thevenin?s equivalent of the system feeding the foult as explained below.

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Assume fault impedance as Z
f
. TH=he thevenin?s eqivalent of the system feeding the faulf impedance is given in
figure 5.5.

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Step: 3
Fig.5 Thevenin?s Equivalent of the system feeding the fault
Obtain the Thevenin?s Equivalent network

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Result:
Thus, the modeling and analysis of power systems under faulted condition and to compute the fault level, post-fault
voltages and currents for different types of faults were obtained using MATLAB.
Outcome:
By doing the experiment, the fault analysis in power system has been done using MATLAB and different types of

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faults have been solved using MATLAB.
Application:
Short Circuit Analysis is performed to determine the currents that flow in a power system under fault
conditions.A Short Circuit Analysis will help to ensure that personnel and equipment are protected by
establishing proper interrupting ratings of protective devices

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1. What is meant by fault?
In an electric power system, a fault or fault current is any abnormal electric current. For example, a short circuit is a fault in
which current bypasses the normal load.

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2. What are the different types of fault?
LG, LL ,LLG and symmetrical fault

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3. What are the assumptions made in fault analysis?
Transformers are on nominal tap position. This will let us take nominal voltages of transformers in
calculations.
All sources are balanced and equal in magnitude and phase. We neglect the slight differences in

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magnitude and phase of the source voltages as it is nothing when compared with the fault.
4. What is meant by bolted fault?
Bolted fault. Notionally, all the conductors are considered connected to ground as if by a metallic conductor; this is called a
"bolted fault
5. What are the different sequence networks in power system?

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Positive sequence, negative sequence and zero sequence
6. Why does fault occur in a power system?
An open-circuit fault occurs if a circuit is interrupted by some failure. ... In a "ground fault" or "earth fault", current flows into
the earth
7. How are the faults classified?

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Symmetrical and unsymmetrical fault
8. List out the various types of shunt and series faults.

Open conductor fault and symmetrical fault
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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
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Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
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% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2

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Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec

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Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.

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(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b

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4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY

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ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-

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Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1

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=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were

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analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?

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The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a

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power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging

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with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle

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The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?

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9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:

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To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6
Theory:

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Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1

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(k)
, PG 2
(k)
, ?PG N
(K)

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}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:

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Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.

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4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;

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warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;

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delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;

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while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));

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dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda

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p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:

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Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =

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8.5000
p =
400.0000
250.0000
150.0000

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Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2

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; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW

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100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc

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n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;

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for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;

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for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg

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for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))

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Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end
end

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Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)

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x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n

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x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n

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Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end
end
Pg

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Output:
lambda =
8.6149
Pg =
367.4040 379.4361 178.1598

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Pg =
350.0000 379.4361 178.1598
Demand new =
575
Lambda new =

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8.7147
Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were

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obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:
Used in power system with lowest cost and schedule with generating unit

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1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.

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3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint

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5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints

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7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:

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Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not

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included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:

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- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

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Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)

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For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.

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Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.

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2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve

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The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle

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Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-

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SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:

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MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and

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phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &

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steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;

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Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate

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sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));

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Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else
Q(i)= Q max(i)

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Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program

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Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run

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5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor

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values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

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Program:
clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')

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nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
PG=[0 .5 .4 .2];

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QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;
for i=1:nb

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Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;

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end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

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end
B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);

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end
c=V(p)*(A+B);
Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt

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Qg=Q*j;
Vt(p)=V(p);
else
if(Q<=Qmin)
Q=Qmin;

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else
Q=Qmax;
end
Vt(p)=1;
disp('it is load bus')

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Qg=Q*j
end
QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);

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end
B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end

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C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;

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for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))

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end
p=p+1;
end
Output:
Y bus =

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2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i

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Q =
0.1456, it is load bus
Q g =
0 + 0.1200i

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V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52



1. What is meant by load flow analysis?

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Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor

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3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators

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5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.

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Simplicity in technique
Small computer memory requirement
Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses

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9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD

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Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:
MATLAB 7.6
Theory:

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The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive

--- Content provided by FirstRanker.com ---

power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.

--- Content provided by FirstRanker.com ---

[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate

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P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max

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End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

Step 7: Change from specified Value
Declare dPa= Psp-P

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dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1

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Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses

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Step 13: Display the output
Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.

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Bus
Real load
demand, P D
Reactive Load
demand, Q D

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Real power
Generation, P G
Reactive Power
Generation, Q G
Voltage

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Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

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2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD
clc
clear all

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sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')

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Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i);
y(i)=(sa(i));

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Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end

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Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q
v=[1.06 1 1];

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

P=[0 0 0];
Q=[0 0 0];
del=[0 0 0];

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Pg=[0 0.2 0];
Pd=[0 0 0.6];
Qg=[0 0 0];
Qd=[0 0 0.25];
for p=2:nb

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for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);

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delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);
end
end
P;

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Q;
Pspe;
Qspe;
delP;
delQ;

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%Calculation of J1
P2=[0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb
if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));

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PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

end
end

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else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end

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PV;
% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
for j=1:nb
if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end

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end
else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end
end

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end
Pdel;
%Calculation of J3
Q2=[0 0 0];
for p=2:nb

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for q=2:nb
if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb
if (j~=p)

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Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 58

end

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end
else
QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));
end
end

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end
QV;
%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb
if(j~=p)

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Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end
end
else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
Qdel;
%Jacobian matrix

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PV(1,:)=[ ];
PV(:,1)=[ ];
Pdel(1,:)=[ ];
Pdel(:,1)=[ ];
QV(1,:)=[ ];

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QV(:,1)=[ ];
Qdel(1,:)=[ ];
Qdel(:,1)=[ ];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 59

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J=[PV Pdel;QV Qdel]
%Find the change in v&del
delP(1:1)=[];
delQ(1:1)=[];
delpq=[delP';delQ']

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vdel=inv(J)*delpq
%Find new v&del
for i=1:nb-1
for j=2:nb
vnew(i)=v(j)+vdel(i);

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delnew(i)=del(j)+vdel(i+2);
end
end
VNEW=[v(1) vnew]
DELNEW=[del(1) delnew

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Output:
Ybus =
6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i
-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i

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J =
2.8420 -1.6670 8.9750 -5.0000
-1.6670 6.3670 -5.0000 20.9000
8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670

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delpq =
0.2750
-0.3000
0.2250
0.6500

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vdel =
0.0575
0.0410
0.0088
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 60

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Viva - voce
-0.0201
VNEW =
1.0600 1.0575 1.0410

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DELNEW =
0 0.0088 -0.0201
Result:
Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of
small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.
Application:
The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By
accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two

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models with viscosity constant and variable across the oil film were developed.


1. What is meant by jacobian matrix?
Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square

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matrix, both the matrix
2. What are the different types of buses in power system network?
Slack bus, generator bus and load bus
3. What are the information obtained from a load flow study?
The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each

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bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.
4. What is the need for load flow study?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating
conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are

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commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?
P.Q,V,?
6. Define - Voltage Controlled Bus
Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled

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through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 61

The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular

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differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with
maximum real power.


8. What is meant by flat voltage start?

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The value of flat voltage start 1+j0
9. What are the advantages of Newton Raphson method?
Newton Raphson method needs less number of iterations to reach convergence, takes less
computation time
More accurate and not sensitive to the factors such like slack bus selection, regulation transformers

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etc. and the number of iterations required in this method is almost independent of system size.
10. What are the disadvantages of Newton Raphson method?
More calculations involved in each iteration and require large computation time per iteration and
large computer memory
Difficult solution technique (programming is difficult)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 62

Expt.No.12: FAULT ANALYSIS IN POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of power systems under faulted condition and to compute the fault
level, post-fault voltages and currents for different types of faults, both symmetric and unsymmetrical. To calculate
the fault current, post fault voltage and fault current through the branches for a three phase to ground fault in a small
power system and also study the effect of neighboring system. Check the results using available software. To obtain

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the fault current, fault MVA, Post-fault bus voltages and fault current distribution for single line to ground fault, line-to-
line fault and double line to ground fault for a small power system, using the available software.To Carryout fault
analysis for a sample power system for LLLG, LG, LL and LLG faults and prepare the report
Software required:
MATLAB 7.6

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Theory:
Short circuit studies are performed to determine bus voltages and currents flowing in different parts the system
when it is subjected to a fault. The current flowing immediately after the fault consists of an AC component which
eventually reaches steady state and a fast decaying DC component which decays to zero. Only the AC component is
considered in the analysis. The analysis is done using phasor technique assuming the system to be under quasi-

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steady state and is done for various types of faults such as three-phase-to ground, line-to-ground, line-to-line and
double-line-to-ground. The results of fault studies are used to select the circuit breakers, set protective relays and to
assess the voltage dips during fault. It is one of the primary studies to be performed whenever system expansion is
planned.
Modeling details:

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Approximations:
The following approximations are usually made in fault analysis:
1. Pre-fault load currents are neglected
2. Transformer taps are assumed to be nominal
3. A symmetric three phase power system is considered

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4. Transmission line shunt capacitance and transformer magnetizing impedances are ignored
5. Series resistances of transmission lines are neglected
6. The negative sequence impedance of alternators is assumed to be the same as their positive sequence
impedance
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 63

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In the case of symmetrical faults, it is sufficient to determine the currents and voltages in one phase. Hence the
analysis is carried out on per phase basis (using + ve sequence Impedance network). In the case of unsymmetrical
faults, the method of symmetrical components is used.
Sequence impedances of power system components:

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The sequence impedances of power system components namely generators, transmission lines and transformers
are required for modeling and analysis of unsymmetrical faults. In the case of overhead transmission lines the
positive-and negative-sequence impedances are the same and the zero sequence impedance depends on ground
wire, tower footing resistance and grounding adopted.
In the case of transformers, the positive-and negative- sequence impedances are the same and the zero

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sequence impedance depends on transformer winding connection, method of neutral grounding and transformer type
(shell or core).The positive-, negative-and zero-sequence impedances are different in the case of rotating equipment
like synchronous generator, synchronous motor and induction motors. Estimation of sequence impedances of the
components and assembling of zero-, positive-and negative-sequence impedance networks are the major steps in
unsymmetrical fault analysis.

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Short circuit computation:
Symmetrical fault analysis:
Since the fault is symmetric the analysis is carried out on per phase basis. A short circuit represents a structural
change in the network which is equivalent to the addition of impedance (in the case of a symmetric short, three equal
impedances) at the location of fault. The changes in voltages and currents that result from this structural change can

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be analyzed using Thevenin?s theorem which states: The changes that occur in the network voltages and currents
due to the addition of an impedance between two network nodes are identical with those voltages and currents that
would be caused by an emf placed in series with the impedance and having a magnitude and polarity equal to the
pre-fault voltage that existed between the nodes in question and all other sources being zeroed. The post-fault
voltages and currents in the network are obtained by superposing these changes on the pre-fault voltages and

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currents.
Example1:
For the two-bus system shown in Fig .1, determine the fault current at the fault point and in other elements for a
fault at bus 2 with a fault impedance Z f . Load current can be assumed to be negligible. The pre-fault voltages at all
the buses can be assumed to be 1.0 p.u. The sub transient reactance of the generators and positive sequence

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reactance of other elements are given. Assume that the resistances of all the elements are negligible.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 64

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Fig 1 Symmetrical fault on a two bus system


First the ?Thevenin?s equivalent network? is formed Fig. 2a). The pre-fault voltage at bus2, V o2 equals 1.0 p.u. In
Fig 2a) the ?Thevenin?s emf? E th= V o2 = 1.0 is inserted in series with the short-circuit branch. The reduced Thevenin?s

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equivalent circuit is given in Fig 2c). In which the ?Thevenin?s equivalent impedance ?Z th is found to be j0.144p.u. It
should be noted that Z th is nothing but the driving point impedance at bus 2 which is the same as the diagonal
element Z 22 of bus impedance matrix of the network. With reference to Fig 2c). The fault current is given by

Fig. 2a)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 65

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Fig. 2b)

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Fig. 2c) Development of thevenin?s equivalent circuit (all impedances are in per unit)

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This current is the total fault current fed by both the generators. The contribution from each generator can be
computed by noting that the total current divides in inverse impedance ratio.
Interconnections with neighboring systems:
If a power system A, is interconnected to a neighboring system B, through, say a tie-line T 12, then for a fault at any
of the buses in system A all the generators in system B also will feed the fault through the tie-line. Instead of

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representing the complete network of the system B, the Thevenin?s equivalent circuit of system B can be connected
at the tie bus 2, (Fig 5.3).
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 66

The Thevenin?s equivalent reactance at bus 2 is given by

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X Th, B = 1/SCC 2
Where SCC 2 is the fault level of Bus2.
Thevenin?s source E Th, B may be assumed as 1.0 p.u

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Fig. 3 Thevenin?s equivalent for neighboring system

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Systematic computation for large scale systems:
The systematic computation procedure to be used for fault analysis of a large power systems using computer is
explained below. Let us consider a symmetric fault at bus r of an n-bus system. Let us assume that the pre-fault
currents are negligible.
Step: 1

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Draw the pre-fault per phase network of the system (positive sequence network) (Fig 5.4).Obtain the positive
sequence bus impedance matrix Z using Building Algorithm. All the machine reactance should be included in the Z
bus.

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Fig 4 Pre-fault per phase network (with loads neglected)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 67

Viva - voce

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Step: 2
Obtain the falut current using the Thevenin?s equivalent of the system feeding the foult as explained below.
Assume fault impedance as Z
f
. TH=he thevenin?s eqivalent of the system feeding the faulf impedance is given in

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figure 5.5.



Step: 3

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Fig.5 Thevenin?s Equivalent of the system feeding the fault
Obtain the Thevenin?s Equivalent network
Result:
Thus, the modeling and analysis of power systems under faulted condition and to compute the fault level, post-fault
voltages and currents for different types of faults were obtained using MATLAB.

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Outcome:
By doing the experiment, the fault analysis in power system has been done using MATLAB and different types of
faults have been solved using MATLAB.
Application:
Short Circuit Analysis is performed to determine the currents that flow in a power system under fault

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conditions.A Short Circuit Analysis will help to ensure that personnel and equipment are protected by
establishing proper interrupting ratings of protective devices


1. What is meant by fault?

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In an electric power system, a fault or fault current is any abnormal electric current. For example, a short circuit is a fault in
which current bypasses the normal load.
2. What are the different types of fault?
LG, LL ,LLG and symmetrical fault

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 68


3. What are the assumptions made in fault analysis?
Transformers are on nominal tap position. This will let us take nominal voltages of transformers in

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calculations.
All sources are balanced and equal in magnitude and phase. We neglect the slight differences in
magnitude and phase of the source voltages as it is nothing when compared with the fault.
4. What is meant by bolted fault?
Bolted fault. Notionally, all the conductors are considered connected to ground as if by a metallic conductor; this is called a

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"bolted fault
5. What are the different sequence networks in power system?
Positive sequence, negative sequence and zero sequence
6. Why does fault occur in a power system?
An open-circuit fault occurs if a circuit is interrupted by some failure. ... In a "ground fault" or "earth fault", current flows into

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the earth
7. How are the faults classified?
Symmetrical and unsymmetrical fault
8. List out the various types of shunt and series faults.

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Open conductor fault and symmetrical fault
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 69

Expt.No.13: MODELING OF FACTS DEVICES USING
SIMULINK

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Aim:
To simulate Facts device in order to control the reactive power flow in a line for efficient operation of the power
system and transmission network
Software required:

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MATLAB /SIMULINK
Theory:
Today?s power grids are driven closer to their transfer capacities due to the increased consumption and power
transfers, endangering the security of the system. Flexible AC transmission systems (FACTS) have gained a great
interest during the last few years, due to recent advances in power electronics. On the other hand, FACTS devices

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are a powerful technology that can solve many outstanding problems in power systems. FACTS devices have been
mainly used for solving various power system steady state control problems such as voltage regulation, power flow
control, and transfer capability enhancement. e.g. by improving the voltage profile or increasing the transfer capacity
of a system without the need of new lines Generally, it is not cost-effective to install FACTS devices for the sole
purpose of power system stability enhancement.

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Overview:
There are two generations for realization of power electronics-based FACTS controllers: the first generation
employs conventional thyristor-switched capacitors and reactors, and quadrature tap-changing transformers, the
second generation employs gate turn-off (GTO) thyristor-switched converters as voltage source converters (VSC?s).
The thyristor-controlled group employs capacitor and reactor banks with fast solid-state switches in traditional shunt

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or series circuit arrangements. The thyristor switches control the on and off periods of the fixed capacitor and reactor
banks and thereby realize a variable reactive impedance. Except for losses, they cannot exchange real power with
the system. The voltage source converter (VSC) type FACTS controller group employs self-commutated DC to AC
converters, using GTO thyristors, which can internally generate capacitive and inductive reactive power for
transmission line compensation, without the use of capacitor or reactor banks. The converter with energy storage

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device can also exchange real power with the system, in addition to the independently controllable reactive power.
The VSC can be used uniformly to control transmission line voltage, impedance, and angle by providing reactive
shunt compensation, series compensation, and phase shifting, or to control directly the real and reactive power flow
in the line.
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

--- Content provided by FirstRanker.com ---

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
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Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2

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Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec

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Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.

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(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b

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4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY

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ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-

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Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1

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=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were

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analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?

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The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a

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power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging

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with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle

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The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?

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9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:

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To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6
Theory:

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Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1

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(k)
, PG 2
(k)
, ?PG N
(K)

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}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:

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Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.

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4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;

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warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;

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delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;

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while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));

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dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda

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p
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totalcost=sum(c+b.*p+a.*p.^2)
Output:

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Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =

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8.5000
p =
400.0000
250.0000
150.0000

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Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2

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; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW

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100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc

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n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;

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for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;

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for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg

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for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))

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Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end
end

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Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)

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x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n

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x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n

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Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end
end
Pg

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Output:
lambda =
8.6149
Pg =
367.4040 379.4361 178.1598

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Pg =
350.0000 379.4361 178.1598
Demand new =
575
Lambda new =

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8.7147
Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were

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obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:
Used in power system with lowest cost and schedule with generating unit

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1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.

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3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint

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5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints

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7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:

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Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not

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included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:

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- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

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Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)

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For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.

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Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.

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2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve

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The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle

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Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-

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SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:

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MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and

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phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &

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steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;

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Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate

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sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));

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Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else
Q(i)= Q max(i)

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Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program

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Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run

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5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor

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values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

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Program:
clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')

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nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
PG=[0 .5 .4 .2];

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QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;
for i=1:nb

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Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;

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end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

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end
B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);

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end
c=V(p)*(A+B);
Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt

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Qg=Q*j;
Vt(p)=V(p);
else
if(Q<=Qmin)
Q=Qmin;

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else
Q=Qmax;
end
Vt(p)=1;
disp('it is load bus')

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Qg=Q*j
end
QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);

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end
B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end

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C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1

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A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;

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for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))

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end
p=p+1;
end
Output:
Y bus =

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2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i

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Q =
0.1456, it is load bus
Q g =
0 + 0.1200i

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V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52



1. What is meant by load flow analysis?

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Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor

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3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators

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5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.

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Simplicity in technique
Small computer memory requirement
Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses

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9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD

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Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:
MATLAB 7.6
Theory:

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The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive

--- Content provided by FirstRanker.com ---

power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.

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[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate

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P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max

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End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

Step 7: Change from specified Value
Declare dPa= Psp-P

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dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1

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Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses

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Step 13: Display the output
Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.

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Bus
Real load
demand, P D
Reactive Load
demand, Q D

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Real power
Generation, P G
Reactive Power
Generation, Q G
Voltage

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Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

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2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD
clc
clear all

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sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')

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Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i);
y(i)=(sa(i));

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Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end

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Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q
v=[1.06 1 1];

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

P=[0 0 0];
Q=[0 0 0];
del=[0 0 0];

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Pg=[0 0.2 0];
Pd=[0 0 0.6];
Qg=[0 0 0];
Qd=[0 0 0.25];
for p=2:nb

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for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);

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delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);
end
end
P;

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Q;
Pspe;
Qspe;
delP;
delQ;

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%Calculation of J1
P2=[0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb
if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));

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PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

end
end

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else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end

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PV;
% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
for j=1:nb
if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end

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end
else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end
end

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end
Pdel;
%Calculation of J3
Q2=[0 0 0];
for p=2:nb

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for q=2:nb
if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb
if (j~=p)

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Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 58

end

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end
else
QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));
end
end

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end
QV;
%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb
if(j~=p)

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Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end
end
else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
Qdel;
%Jacobian matrix

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PV(1,:)=[ ];
PV(:,1)=[ ];
Pdel(1,:)=[ ];
Pdel(:,1)=[ ];
QV(1,:)=[ ];

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QV(:,1)=[ ];
Qdel(1,:)=[ ];
Qdel(:,1)=[ ];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 59

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J=[PV Pdel;QV Qdel]
%Find the change in v&del
delP(1:1)=[];
delQ(1:1)=[];
delpq=[delP';delQ']

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vdel=inv(J)*delpq
%Find new v&del
for i=1:nb-1
for j=2:nb
vnew(i)=v(j)+vdel(i);

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delnew(i)=del(j)+vdel(i+2);
end
end
VNEW=[v(1) vnew]
DELNEW=[del(1) delnew

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Output:
Ybus =
6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i
-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i

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J =
2.8420 -1.6670 8.9750 -5.0000
-1.6670 6.3670 -5.0000 20.9000
8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670

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delpq =
0.2750
-0.3000
0.2250
0.6500

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vdel =
0.0575
0.0410
0.0088
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 60

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Viva - voce
-0.0201
VNEW =
1.0600 1.0575 1.0410

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DELNEW =
0 0.0088 -0.0201
Result:
Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of
small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.
Application:
The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By
accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two

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models with viscosity constant and variable across the oil film were developed.


1. What is meant by jacobian matrix?
Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square

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matrix, both the matrix
2. What are the different types of buses in power system network?
Slack bus, generator bus and load bus
3. What are the information obtained from a load flow study?
The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each

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bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.
4. What is the need for load flow study?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating
conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are

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commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?
P.Q,V,?
6. Define - Voltage Controlled Bus
Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled

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through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?
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The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular

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differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with
maximum real power.


8. What is meant by flat voltage start?

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The value of flat voltage start 1+j0
9. What are the advantages of Newton Raphson method?
Newton Raphson method needs less number of iterations to reach convergence, takes less
computation time
More accurate and not sensitive to the factors such like slack bus selection, regulation transformers

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etc. and the number of iterations required in this method is almost independent of system size.
10. What are the disadvantages of Newton Raphson method?
More calculations involved in each iteration and require large computation time per iteration and
large computer memory
Difficult solution technique (programming is difficult)

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Expt.No.12: FAULT ANALYSIS IN POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of power systems under faulted condition and to compute the fault
level, post-fault voltages and currents for different types of faults, both symmetric and unsymmetrical. To calculate
the fault current, post fault voltage and fault current through the branches for a three phase to ground fault in a small
power system and also study the effect of neighboring system. Check the results using available software. To obtain

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the fault current, fault MVA, Post-fault bus voltages and fault current distribution for single line to ground fault, line-to-
line fault and double line to ground fault for a small power system, using the available software.To Carryout fault
analysis for a sample power system for LLLG, LG, LL and LLG faults and prepare the report
Software required:
MATLAB 7.6

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Theory:
Short circuit studies are performed to determine bus voltages and currents flowing in different parts the system
when it is subjected to a fault. The current flowing immediately after the fault consists of an AC component which
eventually reaches steady state and a fast decaying DC component which decays to zero. Only the AC component is
considered in the analysis. The analysis is done using phasor technique assuming the system to be under quasi-

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steady state and is done for various types of faults such as three-phase-to ground, line-to-ground, line-to-line and
double-line-to-ground. The results of fault studies are used to select the circuit breakers, set protective relays and to
assess the voltage dips during fault. It is one of the primary studies to be performed whenever system expansion is
planned.
Modeling details:

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Approximations:
The following approximations are usually made in fault analysis:
1. Pre-fault load currents are neglected
2. Transformer taps are assumed to be nominal
3. A symmetric three phase power system is considered

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4. Transmission line shunt capacitance and transformer magnetizing impedances are ignored
5. Series resistances of transmission lines are neglected
6. The negative sequence impedance of alternators is assumed to be the same as their positive sequence
impedance
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 63

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In the case of symmetrical faults, it is sufficient to determine the currents and voltages in one phase. Hence the
analysis is carried out on per phase basis (using + ve sequence Impedance network). In the case of unsymmetrical
faults, the method of symmetrical components is used.
Sequence impedances of power system components:

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The sequence impedances of power system components namely generators, transmission lines and transformers
are required for modeling and analysis of unsymmetrical faults. In the case of overhead transmission lines the
positive-and negative-sequence impedances are the same and the zero sequence impedance depends on ground
wire, tower footing resistance and grounding adopted.
In the case of transformers, the positive-and negative- sequence impedances are the same and the zero

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sequence impedance depends on transformer winding connection, method of neutral grounding and transformer type
(shell or core).The positive-, negative-and zero-sequence impedances are different in the case of rotating equipment
like synchronous generator, synchronous motor and induction motors. Estimation of sequence impedances of the
components and assembling of zero-, positive-and negative-sequence impedance networks are the major steps in
unsymmetrical fault analysis.

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Short circuit computation:
Symmetrical fault analysis:
Since the fault is symmetric the analysis is carried out on per phase basis. A short circuit represents a structural
change in the network which is equivalent to the addition of impedance (in the case of a symmetric short, three equal
impedances) at the location of fault. The changes in voltages and currents that result from this structural change can

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be analyzed using Thevenin?s theorem which states: The changes that occur in the network voltages and currents
due to the addition of an impedance between two network nodes are identical with those voltages and currents that
would be caused by an emf placed in series with the impedance and having a magnitude and polarity equal to the
pre-fault voltage that existed between the nodes in question and all other sources being zeroed. The post-fault
voltages and currents in the network are obtained by superposing these changes on the pre-fault voltages and

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currents.
Example1:
For the two-bus system shown in Fig .1, determine the fault current at the fault point and in other elements for a
fault at bus 2 with a fault impedance Z f . Load current can be assumed to be negligible. The pre-fault voltages at all
the buses can be assumed to be 1.0 p.u. The sub transient reactance of the generators and positive sequence

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reactance of other elements are given. Assume that the resistances of all the elements are negligible.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 64

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Fig 1 Symmetrical fault on a two bus system


First the ?Thevenin?s equivalent network? is formed Fig. 2a). The pre-fault voltage at bus2, V o2 equals 1.0 p.u. In
Fig 2a) the ?Thevenin?s emf? E th= V o2 = 1.0 is inserted in series with the short-circuit branch. The reduced Thevenin?s

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equivalent circuit is given in Fig 2c). In which the ?Thevenin?s equivalent impedance ?Z th is found to be j0.144p.u. It
should be noted that Z th is nothing but the driving point impedance at bus 2 which is the same as the diagonal
element Z 22 of bus impedance matrix of the network. With reference to Fig 2c). The fault current is given by

Fig. 2a)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 65

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Fig. 2b)

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Fig. 2c) Development of thevenin?s equivalent circuit (all impedances are in per unit)

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This current is the total fault current fed by both the generators. The contribution from each generator can be
computed by noting that the total current divides in inverse impedance ratio.
Interconnections with neighboring systems:
If a power system A, is interconnected to a neighboring system B, through, say a tie-line T 12, then for a fault at any
of the buses in system A all the generators in system B also will feed the fault through the tie-line. Instead of

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representing the complete network of the system B, the Thevenin?s equivalent circuit of system B can be connected
at the tie bus 2, (Fig 5.3).
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The Thevenin?s equivalent reactance at bus 2 is given by

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X Th, B = 1/SCC 2
Where SCC 2 is the fault level of Bus2.
Thevenin?s source E Th, B may be assumed as 1.0 p.u

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Fig. 3 Thevenin?s equivalent for neighboring system

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Systematic computation for large scale systems:
The systematic computation procedure to be used for fault analysis of a large power systems using computer is
explained below. Let us consider a symmetric fault at bus r of an n-bus system. Let us assume that the pre-fault
currents are negligible.
Step: 1

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Draw the pre-fault per phase network of the system (positive sequence network) (Fig 5.4).Obtain the positive
sequence bus impedance matrix Z using Building Algorithm. All the machine reactance should be included in the Z
bus.

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Fig 4 Pre-fault per phase network (with loads neglected)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 67

Viva - voce

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Step: 2
Obtain the falut current using the Thevenin?s equivalent of the system feeding the foult as explained below.
Assume fault impedance as Z
f
. TH=he thevenin?s eqivalent of the system feeding the faulf impedance is given in

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figure 5.5.



Step: 3

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Fig.5 Thevenin?s Equivalent of the system feeding the fault
Obtain the Thevenin?s Equivalent network
Result:
Thus, the modeling and analysis of power systems under faulted condition and to compute the fault level, post-fault
voltages and currents for different types of faults were obtained using MATLAB.

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Outcome:
By doing the experiment, the fault analysis in power system has been done using MATLAB and different types of
faults have been solved using MATLAB.
Application:
Short Circuit Analysis is performed to determine the currents that flow in a power system under fault

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conditions.A Short Circuit Analysis will help to ensure that personnel and equipment are protected by
establishing proper interrupting ratings of protective devices


1. What is meant by fault?

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In an electric power system, a fault or fault current is any abnormal electric current. For example, a short circuit is a fault in
which current bypasses the normal load.
2. What are the different types of fault?
LG, LL ,LLG and symmetrical fault

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 68


3. What are the assumptions made in fault analysis?
Transformers are on nominal tap position. This will let us take nominal voltages of transformers in

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calculations.
All sources are balanced and equal in magnitude and phase. We neglect the slight differences in
magnitude and phase of the source voltages as it is nothing when compared with the fault.
4. What is meant by bolted fault?
Bolted fault. Notionally, all the conductors are considered connected to ground as if by a metallic conductor; this is called a

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"bolted fault
5. What are the different sequence networks in power system?
Positive sequence, negative sequence and zero sequence
6. Why does fault occur in a power system?
An open-circuit fault occurs if a circuit is interrupted by some failure. ... In a "ground fault" or "earth fault", current flows into

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the earth
7. How are the faults classified?
Symmetrical and unsymmetrical fault
8. List out the various types of shunt and series faults.

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Open conductor fault and symmetrical fault
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 69

Expt.No.13: MODELING OF FACTS DEVICES USING
SIMULINK

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Aim:
To simulate Facts device in order to control the reactive power flow in a line for efficient operation of the power
system and transmission network
Software required:

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MATLAB /SIMULINK
Theory:
Today?s power grids are driven closer to their transfer capacities due to the increased consumption and power
transfers, endangering the security of the system. Flexible AC transmission systems (FACTS) have gained a great
interest during the last few years, due to recent advances in power electronics. On the other hand, FACTS devices

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are a powerful technology that can solve many outstanding problems in power systems. FACTS devices have been
mainly used for solving various power system steady state control problems such as voltage regulation, power flow
control, and transfer capability enhancement. e.g. by improving the voltage profile or increasing the transfer capacity
of a system without the need of new lines Generally, it is not cost-effective to install FACTS devices for the sole
purpose of power system stability enhancement.

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Overview:
There are two generations for realization of power electronics-based FACTS controllers: the first generation
employs conventional thyristor-switched capacitors and reactors, and quadrature tap-changing transformers, the
second generation employs gate turn-off (GTO) thyristor-switched converters as voltage source converters (VSC?s).
The thyristor-controlled group employs capacitor and reactor banks with fast solid-state switches in traditional shunt

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or series circuit arrangements. The thyristor switches control the on and off periods of the fixed capacitor and reactor
banks and thereby realize a variable reactive impedance. Except for losses, they cannot exchange real power with
the system. The voltage source converter (VSC) type FACTS controller group employs self-commutated DC to AC
converters, using GTO thyristors, which can internally generate capacitive and inductive reactive power for
transmission line compensation, without the use of capacitor or reactor banks. The converter with energy storage

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device can also exchange real power with the system, in addition to the independently controllable reactive power.
The VSC can be used uniformly to control transmission line voltage, impedance, and angle by providing reactive
shunt compensation, series compensation, and phase shifting, or to control directly the real and reactive power flow
in the line.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 70

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Series compensation:
In series compensation, the FACTS is connected in series with the power system. It works as a controllable
voltage source. Series inductance occurs in long transmission lines, and when a large current flow causes a large

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voltage drop. To compensate, series capacitors are connected.


Shunt compensation:
Fig 1. Series Compensation

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In shunt compensation, power system is connected in shunt (parallel) with the FACTS. It works as a controllable
current source.

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Fig 2. Shunt Compensation
First generation of Facts devices:
1. Static VAR Compensator (SVC)
2. Thyristor-Controlled Series Capacitor (TCSC)
FirstRanker.com - FirstRanker's Choice

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF

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ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :
Register No. :

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Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

? To provide competent technical manpower capable of meeting requirements of the industry

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? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul

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DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape

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them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity


? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics

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industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices

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MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)

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1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education
2. Core Competence

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To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products

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4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context
5. Lifelong Learning/Ethics

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To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical

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and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits

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d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate

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awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

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COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

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To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks

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3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems

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8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.

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5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.

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9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton

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Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 5

EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS
Sl. No. Name of the experiment Page No.

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CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21

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5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35

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9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58
Mini Project

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13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:

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To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:
1. Introduction to MATLAB:

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MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,

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and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development
? Modeling, simulation and prototype

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? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even

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for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?

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>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will

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probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work

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space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created

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to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.
>> Simulink

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At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.

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1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk

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To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,

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1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.
1.3 MATLAB workspace:

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The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is
>>clear all

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It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;
>>whos

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>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow

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until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:

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The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];
>>whos

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Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply

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by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)

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>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,

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>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:
>>clear all

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>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];
>>B= [6 5; 3 1];

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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.
>>clear all

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>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the

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scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type

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>>help if
>>help for
>>help while
Example :

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]Looping :


>>if z=0

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>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2

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1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,

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>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);

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>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.
1.8 Functions:

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As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :

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>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;
1 4 5] as input, the output would be,

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y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named

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?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z

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return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]
>>admin(z)

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The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated

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themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

Application:

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MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping
Application development, including Graphical User Interface building

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Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?

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The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?
For , while

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5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block

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libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots

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9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

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is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?

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MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and

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visualization

Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES

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PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13

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Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

Step 4: Calculate the Value of Impedance and Capacitance of the line

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Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.

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(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:
%3 phase single circuit

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D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');
r=d/2;

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Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);

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Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink

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conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:
Inductance:

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The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)

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Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :

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GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 17

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.

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Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');

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d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;

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b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;

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Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);

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Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;

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DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)

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Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);

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GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:

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The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

Application :

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 19

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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately

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3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.
4. What is meant by bundling of conductors?

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Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six

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conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost

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7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?
9. What is meant by skin effect?

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Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the

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apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

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Aim:
To perform the modeling and performance of medium transmission lines
Software required:
MATLAB 7.6

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Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.

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Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = re-1/4 = r' = 0.7788 r

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Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:

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A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.

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Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.

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Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application
It is used in transmission and distribution of electrical power system.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?
Single circuit

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Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.

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5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?
2. Nominal T

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7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

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Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

Aim:

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To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:
Formation of Y

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bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent

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circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-

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diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of

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existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.

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Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.

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Step 5: Form the Impedance Z bus matrix.
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Step 6: End the program.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.
5. View the results.

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Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

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Line data:


From To R X B/2

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Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03

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2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025

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3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

Program:

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% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');

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fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...

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z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...

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ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...
for k=1:nbranch

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ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....
for m=1:nbus

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for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end
end

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end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus
Result:

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Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

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Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27

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1. What is meant by singular transformation method?
The matrix formed by graph theory.
2. What is meant by inspection method?

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The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?
Generator, Transformer, transmission line, load

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5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?

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Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?
Resistor and reactor

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10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.
Per unit is defined as the ratio of actual value to base value

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12. What are the advantages of per unit computations?

The manufacture is used as common value

It is easy to understand.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor

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systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.

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Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8

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(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal

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frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1

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An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller

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gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:

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By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency

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constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?

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Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.

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8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM
Aim:

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To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:
MATLAB / SIMULINK

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Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of

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the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result

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Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

Area 1 2

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Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec

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Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.

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(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34

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Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?
a and b

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4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY

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ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-

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Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1

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=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were

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analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact
2. What is meant by transient stability?

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The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a

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power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging

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with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle

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The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?

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9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB
Aim:

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To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6
Theory:

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Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1

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(k)
, PG 2
(k)
, ?PG N
(K)

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}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:

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Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.

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4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

Exercise 1:

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The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2

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2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2
; P 3 in MW

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The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;
clear all;

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warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];
Pd=800;

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delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;

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while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));

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dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end
lambda

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p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)
Output:

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Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0
lambda =

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8.5000
p =
400.0000
250.0000
150.0000

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Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2

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; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW

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100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear
clc

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n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

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c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];
x=0; y=0;

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for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y
Pgtotal=0;

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for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end
Pg

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for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else
if(Pg(i)<=Pmin(i))

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Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end
end

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Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand
demandnew=demand-Pg(1)

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x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

for i=2:n

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x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1
for i=2:n

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Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end
end
Pg

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Output:
lambda =
8.6149
Pg =
367.4040 379.4361 178.1598

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Pg =
350.0000 379.4361 178.1598
Demand new =
575
Lambda new =

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8.7147
Pg =
350.0000 390.5242 184.4758
Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were

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obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:
Used in power system with lowest cost and schedule with generating unit

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1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.

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3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?
Fuel constraint, station constraint

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5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints

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7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system
9. What is meant by participation factor?

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Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:

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Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system

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Software required:
MATLAB 7.6
Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the

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system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is

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said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system

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strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

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Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not

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included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds
(b) Obtain the following time domain plots:

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- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

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Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)

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For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

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Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.

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Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.

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2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

4. Define ? Swing Curve

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The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

6. Define ? Power Angle

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Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-

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SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:

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MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and

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phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &

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steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;

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Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate

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sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));

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Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else
Q(i)= Q max(i)

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Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program

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Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run

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5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor

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values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

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Program:
clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')

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nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl

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k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);

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Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
PG=[0 .5 .4 .2];

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QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;
for i=1:nb

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Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;
Vt(p)=V(p) ;

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end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

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end
B=0;
for q=p:nb
B=B+Ybus(p,q)*V(q);

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end
c=V(p)*(A+B);
Q=-imag(c)

if(Qmin<=Q&&Q<=Qmax)%check for Q limt

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Qg=Q*j;
Vt(p)=V(p);
else
if(Q<=Qmin)
Q=Qmin;

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else
Q=Qmax;
end
Vt(p)=1;
disp('it is load bus')

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Qg=Q*j
end
QG(p)=Qg;
for q=1:p-1
A1=Ybus(p,q)*V(q);

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end
B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));
end

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C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;
for q=1:p-1

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

A2=A2-Ybus(p,q)*Vt(q);
end
B2=0;

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for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end
C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))

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end
p=p+1;
end
Output:
Y bus =

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2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i

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Q =
0.1456, it is load bus
Q g =
0 + 0.1200i

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V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52



1. What is meant by load flow analysis?

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Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor

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3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators

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5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.

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Simplicity in technique
Small computer memory requirement
Less computational time per iteration
8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses

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9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD

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Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:
MATLAB 7.6
Theory:

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The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive

--- Content provided by FirstRanker.com ---

power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.

--- Content provided by FirstRanker.com ---

[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.
Algorithm:

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Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate

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P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2
Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max

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End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

Step 7: Change from specified Value
Declare dPa= Psp-P

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dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3
End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1

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Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses

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Step 13: Display the output
Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.

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Bus
Real load
demand, P D
Reactive Load
demand, Q D

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Real power
Generation, P G
Reactive Power
Generation, Q G
Voltage

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Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

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2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD
clc
clear all

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sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')

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Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i);
y(i)=(sa(i));

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Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end

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Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q
v=[1.06 1 1];

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

P=[0 0 0];
Q=[0 0 0];
del=[0 0 0];

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Pg=[0 0.2 0];
Pd=[0 0 0.6];
Qg=[0 0 0];
Qd=[0 0 0.25];
for p=2:nb

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for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);

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delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);
end
end
P;

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Q;
Pspe;
Qspe;
delP;
delQ;

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%Calculation of J1
P2=[0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb
if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));

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PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

end
end

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else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end

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PV;
% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb

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if(p==q)
for j=1:nb
if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end

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end
else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end
end

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end
Pdel;
%Calculation of J3
Q2=[0 0 0];
for p=2:nb

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for q=2:nb
if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb
if (j~=p)

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Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);
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end

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end
else
QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));
end
end

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end
QV;
%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb
if(j~=p)

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Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end
end
else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
Qdel;
%Jacobian matrix

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PV(1,:)=[ ];
PV(:,1)=[ ];
Pdel(1,:)=[ ];
Pdel(:,1)=[ ];
QV(1,:)=[ ];

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QV(:,1)=[ ];
Qdel(1,:)=[ ];
Qdel(:,1)=[ ];
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J=[PV Pdel;QV Qdel]
%Find the change in v&del
delP(1:1)=[];
delQ(1:1)=[];
delpq=[delP';delQ']

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vdel=inv(J)*delpq
%Find new v&del
for i=1:nb-1
for j=2:nb
vnew(i)=v(j)+vdel(i);

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delnew(i)=del(j)+vdel(i+2);
end
end
VNEW=[v(1) vnew]
DELNEW=[del(1) delnew

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Output:
Ybus =
6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i
-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i

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J =
2.8420 -1.6670 8.9750 -5.0000
-1.6670 6.3670 -5.0000 20.9000
8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670

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delpq =
0.2750
-0.3000
0.2250
0.6500

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vdel =
0.0575
0.0410
0.0088
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 60

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Viva - voce
-0.0201
VNEW =
1.0600 1.0575 1.0410

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DELNEW =
0 0.0088 -0.0201
Result:
Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of
small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.

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Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.
Application:
The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By
accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two

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models with viscosity constant and variable across the oil film were developed.


1. What is meant by jacobian matrix?
Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square

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matrix, both the matrix
2. What are the different types of buses in power system network?
Slack bus, generator bus and load bus
3. What are the information obtained from a load flow study?
The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each

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bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.
4. What is the need for load flow study?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating
conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are

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commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?
P.Q,V,?
6. Define - Voltage Controlled Bus
Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled

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through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?
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The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular

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differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with
maximum real power.


8. What is meant by flat voltage start?

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The value of flat voltage start 1+j0
9. What are the advantages of Newton Raphson method?
Newton Raphson method needs less number of iterations to reach convergence, takes less
computation time
More accurate and not sensitive to the factors such like slack bus selection, regulation transformers

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etc. and the number of iterations required in this method is almost independent of system size.
10. What are the disadvantages of Newton Raphson method?
More calculations involved in each iteration and require large computation time per iteration and
large computer memory
Difficult solution technique (programming is difficult)

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Expt.No.12: FAULT ANALYSIS IN POWER SYSTEM

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Aim:
To become familiar with modeling and analysis of power systems under faulted condition and to compute the fault
level, post-fault voltages and currents for different types of faults, both symmetric and unsymmetrical. To calculate
the fault current, post fault voltage and fault current through the branches for a three phase to ground fault in a small
power system and also study the effect of neighboring system. Check the results using available software. To obtain

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the fault current, fault MVA, Post-fault bus voltages and fault current distribution for single line to ground fault, line-to-
line fault and double line to ground fault for a small power system, using the available software.To Carryout fault
analysis for a sample power system for LLLG, LG, LL and LLG faults and prepare the report
Software required:
MATLAB 7.6

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Theory:
Short circuit studies are performed to determine bus voltages and currents flowing in different parts the system
when it is subjected to a fault. The current flowing immediately after the fault consists of an AC component which
eventually reaches steady state and a fast decaying DC component which decays to zero. Only the AC component is
considered in the analysis. The analysis is done using phasor technique assuming the system to be under quasi-

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steady state and is done for various types of faults such as three-phase-to ground, line-to-ground, line-to-line and
double-line-to-ground. The results of fault studies are used to select the circuit breakers, set protective relays and to
assess the voltage dips during fault. It is one of the primary studies to be performed whenever system expansion is
planned.
Modeling details:

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Approximations:
The following approximations are usually made in fault analysis:
1. Pre-fault load currents are neglected
2. Transformer taps are assumed to be nominal
3. A symmetric three phase power system is considered

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4. Transmission line shunt capacitance and transformer magnetizing impedances are ignored
5. Series resistances of transmission lines are neglected
6. The negative sequence impedance of alternators is assumed to be the same as their positive sequence
impedance
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In the case of symmetrical faults, it is sufficient to determine the currents and voltages in one phase. Hence the
analysis is carried out on per phase basis (using + ve sequence Impedance network). In the case of unsymmetrical
faults, the method of symmetrical components is used.
Sequence impedances of power system components:

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The sequence impedances of power system components namely generators, transmission lines and transformers
are required for modeling and analysis of unsymmetrical faults. In the case of overhead transmission lines the
positive-and negative-sequence impedances are the same and the zero sequence impedance depends on ground
wire, tower footing resistance and grounding adopted.
In the case of transformers, the positive-and negative- sequence impedances are the same and the zero

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sequence impedance depends on transformer winding connection, method of neutral grounding and transformer type
(shell or core).The positive-, negative-and zero-sequence impedances are different in the case of rotating equipment
like synchronous generator, synchronous motor and induction motors. Estimation of sequence impedances of the
components and assembling of zero-, positive-and negative-sequence impedance networks are the major steps in
unsymmetrical fault analysis.

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Short circuit computation:
Symmetrical fault analysis:
Since the fault is symmetric the analysis is carried out on per phase basis. A short circuit represents a structural
change in the network which is equivalent to the addition of impedance (in the case of a symmetric short, three equal
impedances) at the location of fault. The changes in voltages and currents that result from this structural change can

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be analyzed using Thevenin?s theorem which states: The changes that occur in the network voltages and currents
due to the addition of an impedance between two network nodes are identical with those voltages and currents that
would be caused by an emf placed in series with the impedance and having a magnitude and polarity equal to the
pre-fault voltage that existed between the nodes in question and all other sources being zeroed. The post-fault
voltages and currents in the network are obtained by superposing these changes on the pre-fault voltages and

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currents.
Example1:
For the two-bus system shown in Fig .1, determine the fault current at the fault point and in other elements for a
fault at bus 2 with a fault impedance Z f . Load current can be assumed to be negligible. The pre-fault voltages at all
the buses can be assumed to be 1.0 p.u. The sub transient reactance of the generators and positive sequence

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reactance of other elements are given. Assume that the resistances of all the elements are negligible.
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Fig 1 Symmetrical fault on a two bus system


First the ?Thevenin?s equivalent network? is formed Fig. 2a). The pre-fault voltage at bus2, V o2 equals 1.0 p.u. In
Fig 2a) the ?Thevenin?s emf? E th= V o2 = 1.0 is inserted in series with the short-circuit branch. The reduced Thevenin?s

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equivalent circuit is given in Fig 2c). In which the ?Thevenin?s equivalent impedance ?Z th is found to be j0.144p.u. It
should be noted that Z th is nothing but the driving point impedance at bus 2 which is the same as the diagonal
element Z 22 of bus impedance matrix of the network. With reference to Fig 2c). The fault current is given by

Fig. 2a)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 65

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Fig. 2b)

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Fig. 2c) Development of thevenin?s equivalent circuit (all impedances are in per unit)

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This current is the total fault current fed by both the generators. The contribution from each generator can be
computed by noting that the total current divides in inverse impedance ratio.
Interconnections with neighboring systems:
If a power system A, is interconnected to a neighboring system B, through, say a tie-line T 12, then for a fault at any
of the buses in system A all the generators in system B also will feed the fault through the tie-line. Instead of

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representing the complete network of the system B, the Thevenin?s equivalent circuit of system B can be connected
at the tie bus 2, (Fig 5.3).
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The Thevenin?s equivalent reactance at bus 2 is given by

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X Th, B = 1/SCC 2
Where SCC 2 is the fault level of Bus2.
Thevenin?s source E Th, B may be assumed as 1.0 p.u

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Fig. 3 Thevenin?s equivalent for neighboring system

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Systematic computation for large scale systems:
The systematic computation procedure to be used for fault analysis of a large power systems using computer is
explained below. Let us consider a symmetric fault at bus r of an n-bus system. Let us assume that the pre-fault
currents are negligible.
Step: 1

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Draw the pre-fault per phase network of the system (positive sequence network) (Fig 5.4).Obtain the positive
sequence bus impedance matrix Z using Building Algorithm. All the machine reactance should be included in the Z
bus.

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Fig 4 Pre-fault per phase network (with loads neglected)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 67

Viva - voce

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Step: 2
Obtain the falut current using the Thevenin?s equivalent of the system feeding the foult as explained below.
Assume fault impedance as Z
f
. TH=he thevenin?s eqivalent of the system feeding the faulf impedance is given in

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figure 5.5.



Step: 3

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Fig.5 Thevenin?s Equivalent of the system feeding the fault
Obtain the Thevenin?s Equivalent network
Result:
Thus, the modeling and analysis of power systems under faulted condition and to compute the fault level, post-fault
voltages and currents for different types of faults were obtained using MATLAB.

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Outcome:
By doing the experiment, the fault analysis in power system has been done using MATLAB and different types of
faults have been solved using MATLAB.
Application:
Short Circuit Analysis is performed to determine the currents that flow in a power system under fault

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conditions.A Short Circuit Analysis will help to ensure that personnel and equipment are protected by
establishing proper interrupting ratings of protective devices


1. What is meant by fault?

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In an electric power system, a fault or fault current is any abnormal electric current. For example, a short circuit is a fault in
which current bypasses the normal load.
2. What are the different types of fault?
LG, LL ,LLG and symmetrical fault

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 68


3. What are the assumptions made in fault analysis?
Transformers are on nominal tap position. This will let us take nominal voltages of transformers in

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calculations.
All sources are balanced and equal in magnitude and phase. We neglect the slight differences in
magnitude and phase of the source voltages as it is nothing when compared with the fault.
4. What is meant by bolted fault?
Bolted fault. Notionally, all the conductors are considered connected to ground as if by a metallic conductor; this is called a

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"bolted fault
5. What are the different sequence networks in power system?
Positive sequence, negative sequence and zero sequence
6. Why does fault occur in a power system?
An open-circuit fault occurs if a circuit is interrupted by some failure. ... In a "ground fault" or "earth fault", current flows into

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the earth
7. How are the faults classified?
Symmetrical and unsymmetrical fault
8. List out the various types of shunt and series faults.

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Open conductor fault and symmetrical fault
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 69

Expt.No.13: MODELING OF FACTS DEVICES USING
SIMULINK

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Aim:
To simulate Facts device in order to control the reactive power flow in a line for efficient operation of the power
system and transmission network
Software required:

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MATLAB /SIMULINK
Theory:
Today?s power grids are driven closer to their transfer capacities due to the increased consumption and power
transfers, endangering the security of the system. Flexible AC transmission systems (FACTS) have gained a great
interest during the last few years, due to recent advances in power electronics. On the other hand, FACTS devices

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are a powerful technology that can solve many outstanding problems in power systems. FACTS devices have been
mainly used for solving various power system steady state control problems such as voltage regulation, power flow
control, and transfer capability enhancement. e.g. by improving the voltage profile or increasing the transfer capacity
of a system without the need of new lines Generally, it is not cost-effective to install FACTS devices for the sole
purpose of power system stability enhancement.

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Overview:
There are two generations for realization of power electronics-based FACTS controllers: the first generation
employs conventional thyristor-switched capacitors and reactors, and quadrature tap-changing transformers, the
second generation employs gate turn-off (GTO) thyristor-switched converters as voltage source converters (VSC?s).
The thyristor-controlled group employs capacitor and reactor banks with fast solid-state switches in traditional shunt

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or series circuit arrangements. The thyristor switches control the on and off periods of the fixed capacitor and reactor
banks and thereby realize a variable reactive impedance. Except for losses, they cannot exchange real power with
the system. The voltage source converter (VSC) type FACTS controller group employs self-commutated DC to AC
converters, using GTO thyristors, which can internally generate capacitive and inductive reactive power for
transmission line compensation, without the use of capacitor or reactor banks. The converter with energy storage

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device can also exchange real power with the system, in addition to the independently controllable reactive power.
The VSC can be used uniformly to control transmission line voltage, impedance, and angle by providing reactive
shunt compensation, series compensation, and phase shifting, or to control directly the real and reactive power flow
in the line.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 70

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Series compensation:
In series compensation, the FACTS is connected in series with the power system. It works as a controllable
voltage source. Series inductance occurs in long transmission lines, and when a large current flow causes a large

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voltage drop. To compensate, series capacitors are connected.


Shunt compensation:
Fig 1. Series Compensation

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In shunt compensation, power system is connected in shunt (parallel) with the FACTS. It works as a controllable
current source.

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Fig 2. Shunt Compensation
First generation of Facts devices:
1. Static VAR Compensator (SVC)
2. Thyristor-Controlled Series Capacitor (TCSC)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 71

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3. Thyristor-Controlled Phase Shifter (TCPS)
Second generation of Facts devices:
1. Static Compensator (STATCOM)
2. Static Synchronous Series Compensator (SSSC)

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3. Unified Power Flow Controller (UPFC)
Series compensation:
FACTS for series compensation modify line impedance: X is decreased so as to increase the transmittable active
power. However, more reactive power must be provided.

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Shunt compensation:
Reactive current is injected into the line to maintain voltage magnitude. Transmittable active power is increased but
more reactive power is to be provided.

Simulink block diagram:

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FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1


?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING


EE 6711- POWER SYSTEM SIMULATION LABORATORY

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VII SEMESTER - R 2013

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Name :

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Register No. :
Class :

LABORATORY MANUAL
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

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VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and

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soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING

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To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems
? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and

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ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher
education

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2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth
To provide relevant training and experience to bridge the gap between theory and practice which enables

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them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to
broader social context

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5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

PROGRAMME OUTCOMES (POs)

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a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability
c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical

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and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities
g. To communicate in verbal and written form with fellow engineers and society at large

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h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning
k. To participate and succeed in competitive exams

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES
EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:
1. Computation of Parameters and Modeling of Transmission Lines

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2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis
6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System

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7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.
4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance

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matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability
analysis of SMIB system.

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8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss
siedel method.

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11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi
machine power systems.

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14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
CONTENTS

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Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13
3 Modeling of transmission line parameters 19

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4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32
CYCLE 2 EXPERIMENTS

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8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50
12 Fault analysis in power system 58

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Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB

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Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB
Theory:

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1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary
tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and

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communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation
? Algorithm development

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? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building
MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical

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manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes
1.2 Getting started with MATLAB:

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To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit
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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively.

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Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the
M-file

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M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a
series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined

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function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)
methodology that is used.

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>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink
has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic

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equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations
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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing
helpdesk gives you access to searchable help as well as all the MATLAB manuals.

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>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual
commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common

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data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not
positive.

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1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like
command is

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>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;
>>b=5;

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>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy
in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands

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and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:
>>A=[1 4;6 3];

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>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a
>>A

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Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.
>>B= [3 0 -1; 4 4 2;7 2 11];

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(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001
>>mytime =0:0.001:5;

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Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.
Example:

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>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;
>>b= [1 2; 3 4];

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>>B= [6 5; 3 1];
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>>beta=b+B
The violation of the rules in matrix algebra can be understood by the following example.

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>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B
In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,

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element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :
Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.

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To explore these simply type
>>help if
>>help for
>>help while
Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z
>>end

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>>for n=1:2:10
>>s=s+n^2
>>end

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- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.
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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;
>> y=sin (pi/180 * t);

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To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);
>>ylabel (?Voltage in volts?)

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>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a
pdf manual on handle graphics for those really interested in it.

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1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some
input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s

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usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?
z= [5 2 4;

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1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;
1 0.25 0.2] which is the reciprocal of each elements.

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To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)

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y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;
1 4 5]

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>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2
Otherwise the same function can be called for any times from any script file provided the function M-file is available

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in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.
Result:

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Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics
Modeling, simulation, and prototyping

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Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming
in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

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2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations
4. What are the different looping statements used in MATLAB?

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For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?
Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi

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domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i
8. Explain how polynomials can be represented in MATLAB?

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poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.
10. What is Interpolation and Extrapolation in MATLAB?

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Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?
Control system tool box, power system tool box, communication tool box,

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12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?
Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application

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development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce
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Aim:

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Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and
double circuit transmission lines for different conductor arrangements

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program
Step 2: Get the input values for distance between the conductors and bundle spacing of

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D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File

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3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1
A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have

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a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Program:

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%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');
d=input('enter the value of d: ');

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r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);
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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))
fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);

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fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Exercise:2

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A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.
Calculation:

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Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)

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D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r
Where, r is the radius of conductor

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Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r
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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various

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cases.
Program:
%3 phase double circuit
%3 phase double circuit
S = input('Enter row vector [S11, S22, S33] = ');

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H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');
S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);

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a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;
b2 = S22/2 + j*0;

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c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);
Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);

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Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);
Dc1c2 = abs(c1 - c2);

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DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;

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GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);
DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);

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DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km
C = 0.0556/log(GMD/GMRC) % micro F/km

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Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:
Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double

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circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.
2. What is meant by geometric mean radius?

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GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines
also helps to reduce the system power loss.

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4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling
5. What is meant by double circuit line?

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A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically
used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight

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and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.
8. What is meant by symmetrical spacing?

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9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?
When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-

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section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission
line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load

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is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

Expt.No.3: MODELING OF TRANSMISSION LINE

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PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines
Software required:

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MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can

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be evaluated using the formula.
Formula used:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

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Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.
Step 3: To find the admittance (y) and impedance (z).

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Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Result:

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Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.
Application

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It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load
2. What are the different types of transmission line?

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Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.
4. What is meant by nominal ? method?

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The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?
1. Nominal ?

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2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6
Theory:

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Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every
transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element

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corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus
matrix:

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In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance
matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can

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be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:
Step 1: Start the program.

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Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)
Z bus = inv(Y)

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Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

Step 6: End the program.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by pressing Tools ? Run.

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5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.
(ii) Check the results obtained using MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02
1 4 0.05 0.20 0.02

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1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02
2 6 0.07 0.20 0.025

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3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')
fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')

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linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...
x = linedata(:,4); % Reactance, X...

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b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...
nbus = max(max(fb),max(tb)); % no. of buses...

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nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

% Formation of the Off Diagonal Elements...

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for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end
% Formation of Diagonal Elements....

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for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);
end

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end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix
zbus

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Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus

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admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis
Bus impedance matrix is used to short circuit study

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27


1. What is meant by singular transformation method?
The matrix formed by graph theory.

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2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.
4. What are the components of a power system?

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Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?
loads represented in reactance diagram resistor with reactor.

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7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance
9. What are the elements of the bus impedance matrix?

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Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus
11. Define per unit value.

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Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA

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POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:

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MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power

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supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.

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Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.
4. After forming the block diagram, save the block diagram.

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5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec
Generator inertia constant, H = 5sec, Governor speed regulation = R per unit

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The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

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Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz
(i) Find the steady state frequency deviation in Hz.

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(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2

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sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with
and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.

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Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system
2. What is meant by load frequency control?

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Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple
generators at different power plants, in response to changes in the load

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4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

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6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop
7. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the
AVR dynamics to settle down before they can make themselves felt in the slower load ?

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frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA
POWER SYSTEM

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Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses
Software required:

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MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of
system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.

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A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control
action which adjusts the load - reference set points of selected (regulating) generator ? turbine units

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram
4. After forming the block diagram, save the block diagram

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5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

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Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4
Base power 1000MVA 1000MVA

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Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in
area1.

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(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and

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without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34


Application:
To maintain the power and frequency constant in electrical power system.

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1. What is meant by two area system?
power system is interconnected one where no of generators are connected together and run in unison manner to meet

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the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant
3. What is meant by area frequency response coefficient?

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a and b
4. What are the major control loops used in large generators?
Frequency control loop
Current control loop
5. What is the use of secondary loop?

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Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

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Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

Aim:

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To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:
MATLAB 7.6
Theory:

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Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may

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come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small

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disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.
(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run

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5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:
A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d

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1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =
0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.
Outcome:

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By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically
the entire system remains intact

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2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system
3. What is meant by single machine infinite bus?

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The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is
the maximum time during which a disturbance can be applied without the system losing its stability

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5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its
stability. The aim of this calculation is to determine the characteristics of protections required by the power system.

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7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?
The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more

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than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The
angle between the two is known as the power angle or torque angle

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING
MATLAB

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Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:
MATLAB 7.6

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Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the
total system load PD at a particular interval can be met by different sets of generation schedules

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{PG 1
(k)
, PG 2
(k)
, ?PG N

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(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.
This economic dispatch problem is mathematically stated as an optimization problem.

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Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda
Step 4: Iterate the variables up to feasible solution

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Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting file - new ? M ? File

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3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

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Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;
P 1 in MW

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C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3
2

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; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:
clc;

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clear all;
warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];
c=[500; 400; 200];

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Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')
disp(['lambda P1 P1 P3 delta p delta lambda'])

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iter=0;
while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);
delp=Pd-sum(p);

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J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;
end

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lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

totalcost=sum(c+b.*p+a.*p.^2)

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Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000
8.5000 400.0000 250.0000 150.0000 0 0

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lambda =
8.5000
p =
400.0000
250.0000

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150.0000
Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1

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2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2
; P 2 in MW

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C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:
200 ? P 1 ? 450 MW

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150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:
clear

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clc
n=3;
demand=925;
a=[.0056 .0045 .0079];
b=[4.5 5.2 5.8];

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];
Pmin=[200 250 125];
Pmax=[350 450 225];

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x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));
lambda=(demand+x)/y

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Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);
end

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Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);
else

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if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);
end

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end
Pgtotal=sum(Pg);
end
Pg
if Pgtotal~=demand

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demandnew=demand-Pg(1)
x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

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for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end
lambdanew=(demandnew+x1)/y1

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for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end
end

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Pg
Output:
lambda =
8.6149
Pg =

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367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598
Demand new =
575

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Lambda new =
8.7147
Pg =
350.0000 390.5242 184.4758
Result:

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Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and
without loss conditions.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:
Used in power system with lowest cost and schedule with generating unit

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1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints
2. What is meant by lambda iteration method?

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lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints
4. What are the different constraints in unit commitment?

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Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price
6. What is the objective of economic dispatch problem?

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objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?
Minimum load Base load in power system

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9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems
Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)

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system
Software required:
MATLAB 7.6
Theory:
Transient stability:

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When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more

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machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the

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nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:

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1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run
5. View the results

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system
modelling requirements:

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I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system
for 2.0 seconds

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(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.
(c) Determine the critical clearing time by progressively increasing the fault clearing time.

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Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = inf; X3 = 0.65;

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eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;
eacfault (Pm, E, V, X1, X2, X3)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce
Result:
Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained

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using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming
Application:

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Used to analysis to transient and steady state behavior of generator.



1. What is meant by steady state stability?

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power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

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4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

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6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

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Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple
method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm

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Software required:
MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow
or load-flow studies are important for planning future expansion of power systems as well as in determining the best

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operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-
scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,

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computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to
find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.

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Algorithm:
Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix
Step 4: Calculate P and Q by using formula,

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P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0
Step 6: Check the condition of for loop

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if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)
Else

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Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented
Step 11: Find the angle value angle=180/Pi*angle(v)

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Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.
3 Type and save the program in the editor Window

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4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude
at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances

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are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

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Program:
clc
clear all
sb=[1 1 2 4 3]; %input('Enter the starting bus = ')

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eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);

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for i=1:nl
k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);
Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);

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Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus

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PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;
Qmax=.12;

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for i=1:nb
Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus
p=1;

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Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1
A=Ybus(p,q)*V(q);

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

end
B=0;
for q=p:nb

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B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);
Q=-imag(c)

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if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);
else
if(Q<=Qmin)

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Q=Qmin;
else
Q=Qmax;
end
Vt(p)=1;

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disp('it is load bus')
Qg=Q*j
end
QG(p)=Qg;
for q=1:p-1

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A1=Ybus(p,q)*V(q);
end
B1=0;
for q=p+1:nb
B1=B1-(((Ybus(p,q))*V(q)));

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end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus
A2=0;

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for q=1:p-1
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

A2=A2-Ybus(p,q)*Vt(q);
end

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B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end
C2=(-PG(p)+(QG(p))/V(p));

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Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;
end
Output:

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Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i
0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i

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Q =
0.1456, it is load bus
Q g =

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0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:
Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power

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flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

Application:

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Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52

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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?
Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the

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acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage
4. Define ? Generator Bus

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The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?
acceleration factor value 1.6

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7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement
Less computational time per iteration
8. List the advantages of load flow analysis.

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Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

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z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-

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RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:
MATLAB 7.6

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Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of
power systems as well as in determining the best operation of existing systems. The principal information obtained

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from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical
solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit

--- Content provided by FirstRanker.com ---

fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per
kilowatt hour deliver.

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Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max
Step 4: To calculate P and Q

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Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2
Set for n=2: nbus

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Calculate Q(G), V(n) for Qmin or Q max
End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

Step 7: Change from specified Value

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Declare dPa= Psp-P
dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3
End the Loop

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Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2
Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]

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Step 12: Find line current flow & line Losses
Step 13: Display the output
Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total

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shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus
Real load
demand, P D
Reactive Load

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demand, Q D
Real power
Generation, P G
Reactive Power
Generation, Q G

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Voltage
Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified
3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

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2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD
clc

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clear all
sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')
nb=3; %input(' Enter the number of buses= ')

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sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i);

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y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);

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end
Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);
% Calculation of P and Q

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v=[1.06 1 1];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 56

P=[0 0 0];
Q=[0 0 0];

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del=[0 0 0];
Pg=[0 0.2 0];
Pd=[0 0 0.6];
Qg=[0 0 0];
Qd=[0 0 0.25];

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for p=2:nb
for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));
Pspe(p)=Pg(p)-Pd(p);

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Qspe(p)=Qg(p)-Qd(p);
delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);
end
end

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P;
Q;
Pspe;
Qspe;
delP;

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delQ;

%Calculation of J1
P2=[0 0 0];
for p=2:nb

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for q=2:nb
if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb
if (j~=p)

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P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));
PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

end

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end
else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end

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end
PV;
% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb

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for q=2:nb
if(p==q)
for j=1:nb
if(j~=p)
Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));

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end
end
else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));
end

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end
end
Pdel;
%Calculation of J3
Q2=[0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));
for j=1:nb

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if (j~=p)
Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 58

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end
end
else
QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));
end

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end

end
QV;
%Calculation of J4

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Qdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb

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if(j~=p)
Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end
end
else

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Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end
Qdel;

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%Jacobian matrix
PV(1,:)=[ ];
PV(:,1)=[ ];
Pdel(1,:)=[ ];
Pdel(:,1)=[ ];

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QV(1,:)=[ ];
QV(:,1)=[ ];
Qdel(1,:)=[ ];
Qdel(:,1)=[ ];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 59

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J=[PV Pdel;QV Qdel]
%Find the change in v&del
delP(1:1)=[];
delQ(1:1)=[];

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delpq=[delP';delQ']
vdel=inv(J)*delpq
%Find new v&del
for i=1:nb-1
for j=2:nb

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vnew(i)=v(j)+vdel(i);
delnew(i)=del(j)+vdel(i+2);
end
end
VNEW=[v(1) vnew]

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DELNEW=[del(1) delnew
Output:
Ybus =
6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i
-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i

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-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i
J =
2.8420 -1.6670 8.9750 -5.0000
-1.6670 6.3670 -5.0000 20.9000
8.5250 -5.0000 -2.9920 1.6670

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-5.0000 19.1000 1.6670 -6.9670
delpq =
0.2750
-0.3000
0.2250

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0.6500
vdel =
0.0575
0.0410
0.0088

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 60

Viva - voce
-0.0201
VNEW =

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1.0600 1.0575 1.0410
DELNEW =
0 0.0088 -0.0201
Result:
Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of

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small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.
Application:
The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By

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accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two
models with viscosity constant and variable across the oil film were developed.


1. What is meant by jacobian matrix?

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Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square
matrix, both the matrix
2. What are the different types of buses in power system network?
Slack bus, generator bus and load bus
3. What are the information obtained from a load flow study?

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The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each
bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.
4. What is the need for load flow study?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating

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conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are
commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?
P.Q,V,?
6. Define - Voltage Controlled Bus

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Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled
through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?
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The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular
differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with
maximum real power.

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8. What is meant by flat voltage start?
The value of flat voltage start 1+j0
9. What are the advantages of Newton Raphson method?
Newton Raphson method needs less number of iterations to reach convergence, takes less
computation time

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More accurate and not sensitive to the factors such like slack bus selection, regulation transformers
etc. and the number of iterations required in this method is almost independent of system size.
10. What are the disadvantages of Newton Raphson method?
More calculations involved in each iteration and require large computation time per iteration and
large computer memory

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Difficult solution technique (programming is difficult)


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Expt.No.12: FAULT ANALYSIS IN POWER SYSTEM
Aim:
To become familiar with modeling and analysis of power systems under faulted condition and to compute the fault
level, post-fault voltages and currents for different types of faults, both symmetric and unsymmetrical. To calculate
the fault current, post fault voltage and fault current through the branches for a three phase to ground fault in a small

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power system and also study the effect of neighboring system. Check the results using available software. To obtain
the fault current, fault MVA, Post-fault bus voltages and fault current distribution for single line to ground fault, line-to-
line fault and double line to ground fault for a small power system, using the available software.To Carryout fault
analysis for a sample power system for LLLG, LG, LL and LLG faults and prepare the report
Software required:

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MATLAB 7.6
Theory:
Short circuit studies are performed to determine bus voltages and currents flowing in different parts the system
when it is subjected to a fault. The current flowing immediately after the fault consists of an AC component which
eventually reaches steady state and a fast decaying DC component which decays to zero. Only the AC component is

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considered in the analysis. The analysis is done using phasor technique assuming the system to be under quasi-
steady state and is done for various types of faults such as three-phase-to ground, line-to-ground, line-to-line and
double-line-to-ground. The results of fault studies are used to select the circuit breakers, set protective relays and to
assess the voltage dips during fault. It is one of the primary studies to be performed whenever system expansion is
planned.

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Modeling details:
Approximations:
The following approximations are usually made in fault analysis:
1. Pre-fault load currents are neglected
2. Transformer taps are assumed to be nominal

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3. A symmetric three phase power system is considered
4. Transmission line shunt capacitance and transformer magnetizing impedances are ignored
5. Series resistances of transmission lines are neglected
6. The negative sequence impedance of alternators is assumed to be the same as their positive sequence
impedance

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In the case of symmetrical faults, it is sufficient to determine the currents and voltages in one phase. Hence the
analysis is carried out on per phase basis (using + ve sequence Impedance network). In the case of unsymmetrical
faults, the method of symmetrical components is used.

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Sequence impedances of power system components:
The sequence impedances of power system components namely generators, transmission lines and transformers
are required for modeling and analysis of unsymmetrical faults. In the case of overhead transmission lines the
positive-and negative-sequence impedances are the same and the zero sequence impedance depends on ground
wire, tower footing resistance and grounding adopted.

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In the case of transformers, the positive-and negative- sequence impedances are the same and the zero
sequence impedance depends on transformer winding connection, method of neutral grounding and transformer type
(shell or core).The positive-, negative-and zero-sequence impedances are different in the case of rotating equipment
like synchronous generator, synchronous motor and induction motors. Estimation of sequence impedances of the
components and assembling of zero-, positive-and negative-sequence impedance networks are the major steps in

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unsymmetrical fault analysis.
Short circuit computation:
Symmetrical fault analysis:
Since the fault is symmetric the analysis is carried out on per phase basis. A short circuit represents a structural
change in the network which is equivalent to the addition of impedance (in the case of a symmetric short, three equal

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impedances) at the location of fault. The changes in voltages and currents that result from this structural change can
be analyzed using Thevenin?s theorem which states: The changes that occur in the network voltages and currents
due to the addition of an impedance between two network nodes are identical with those voltages and currents that
would be caused by an emf placed in series with the impedance and having a magnitude and polarity equal to the
pre-fault voltage that existed between the nodes in question and all other sources being zeroed. The post-fault

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voltages and currents in the network are obtained by superposing these changes on the pre-fault voltages and
currents.
Example1:
For the two-bus system shown in Fig .1, determine the fault current at the fault point and in other elements for a
fault at bus 2 with a fault impedance Z f . Load current can be assumed to be negligible. The pre-fault voltages at all

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the buses can be assumed to be 1.0 p.u. The sub transient reactance of the generators and positive sequence
reactance of other elements are given. Assume that the resistances of all the elements are negligible.
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Fig 1 Symmetrical fault on a two bus system


First the ?Thevenin?s equivalent network? is formed Fig. 2a). The pre-fault voltage at bus2, V o2 equals 1.0 p.u. In

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Fig 2a) the ?Thevenin?s emf? E th= V o2 = 1.0 is inserted in series with the short-circuit branch. The reduced Thevenin?s
equivalent circuit is given in Fig 2c). In which the ?Thevenin?s equivalent impedance ?Z th is found to be j0.144p.u. It
should be noted that Z th is nothing but the driving point impedance at bus 2 which is the same as the diagonal
element Z 22 of bus impedance matrix of the network. With reference to Fig 2c). The fault current is given by

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Fig. 2a)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 65

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Fig. 2b)

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Fig. 2c) Development of thevenin?s equivalent circuit (all impedances are in per unit)

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This current is the total fault current fed by both the generators. The contribution from each generator can be
computed by noting that the total current divides in inverse impedance ratio.
Interconnections with neighboring systems:
If a power system A, is interconnected to a neighboring system B, through, say a tie-line T 12, then for a fault at any

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of the buses in system A all the generators in system B also will feed the fault through the tie-line. Instead of
representing the complete network of the system B, the Thevenin?s equivalent circuit of system B can be connected
at the tie bus 2, (Fig 5.3).
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 66

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The Thevenin?s equivalent reactance at bus 2 is given by
X Th, B = 1/SCC 2
Where SCC 2 is the fault level of Bus2.
Thevenin?s source E Th, B may be assumed as 1.0 p.u

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Fig. 3 Thevenin?s equivalent for neighboring system
Systematic computation for large scale systems:
The systematic computation procedure to be used for fault analysis of a large power systems using computer is
explained below. Let us consider a symmetric fault at bus r of an n-bus system. Let us assume that the pre-fault
currents are negligible.

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Step: 1
Draw the pre-fault per phase network of the system (positive sequence network) (Fig 5.4).Obtain the positive
sequence bus impedance matrix Z using Building Algorithm. All the machine reactance should be included in the Z
bus.

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Fig 4 Pre-fault per phase network (with loads neglected)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 67

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Viva - voce
Step: 2
Obtain the falut current using the Thevenin?s equivalent of the system feeding the foult as explained below.
Assume fault impedance as Z
f

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. TH=he thevenin?s eqivalent of the system feeding the faulf impedance is given in
figure 5.5.

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Step: 3
Fig.5 Thevenin?s Equivalent of the system feeding the fault
Obtain the Thevenin?s Equivalent network
Result:
Thus, the modeling and analysis of power systems under faulted condition and to compute the fault level, post-fault

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voltages and currents for different types of faults were obtained using MATLAB.
Outcome:
By doing the experiment, the fault analysis in power system has been done using MATLAB and different types of
faults have been solved using MATLAB.
Application:

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Short Circuit Analysis is performed to determine the currents that flow in a power system under fault
conditions.A Short Circuit Analysis will help to ensure that personnel and equipment are protected by
establishing proper interrupting ratings of protective devices

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1. What is meant by fault?
In an electric power system, a fault or fault current is any abnormal electric current. For example, a short circuit is a fault in
which current bypasses the normal load.
2. What are the different types of fault?
LG, LL ,LLG and symmetrical fault

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 68


3. What are the assumptions made in fault analysis?

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Transformers are on nominal tap position. This will let us take nominal voltages of transformers in
calculations.
All sources are balanced and equal in magnitude and phase. We neglect the slight differences in
magnitude and phase of the source voltages as it is nothing when compared with the fault.
4. What is meant by bolted fault?

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Bolted fault. Notionally, all the conductors are considered connected to ground as if by a metallic conductor; this is called a
"bolted fault
5. What are the different sequence networks in power system?
Positive sequence, negative sequence and zero sequence
6. Why does fault occur in a power system?

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An open-circuit fault occurs if a circuit is interrupted by some failure. ... In a "ground fault" or "earth fault", current flows into
the earth
7. How are the faults classified?
Symmetrical and unsymmetrical fault
8. List out the various types of shunt and series faults.

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Open conductor fault and symmetrical fault
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 69

Expt.No.13: MODELING OF FACTS DEVICES USING

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SIMULINK

Aim:
To simulate Facts device in order to control the reactive power flow in a line for efficient operation of the power
system and transmission network

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Software required:
MATLAB /SIMULINK
Theory:
Today?s power grids are driven closer to their transfer capacities due to the increased consumption and power
transfers, endangering the security of the system. Flexible AC transmission systems (FACTS) have gained a great

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interest during the last few years, due to recent advances in power electronics. On the other hand, FACTS devices
are a powerful technology that can solve many outstanding problems in power systems. FACTS devices have been
mainly used for solving various power system steady state control problems such as voltage regulation, power flow
control, and transfer capability enhancement. e.g. by improving the voltage profile or increasing the transfer capacity
of a system without the need of new lines Generally, it is not cost-effective to install FACTS devices for the sole

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purpose of power system stability enhancement.
Overview:
There are two generations for realization of power electronics-based FACTS controllers: the first generation
employs conventional thyristor-switched capacitors and reactors, and quadrature tap-changing transformers, the
second generation employs gate turn-off (GTO) thyristor-switched converters as voltage source converters (VSC?s).

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The thyristor-controlled group employs capacitor and reactor banks with fast solid-state switches in traditional shunt
or series circuit arrangements. The thyristor switches control the on and off periods of the fixed capacitor and reactor
banks and thereby realize a variable reactive impedance. Except for losses, they cannot exchange real power with
the system. The voltage source converter (VSC) type FACTS controller group employs self-commutated DC to AC
converters, using GTO thyristors, which can internally generate capacitive and inductive reactive power for

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transmission line compensation, without the use of capacitor or reactor banks. The converter with energy storage
device can also exchange real power with the system, in addition to the independently controllable reactive power.
The VSC can be used uniformly to control transmission line voltage, impedance, and angle by providing reactive
shunt compensation, series compensation, and phase shifting, or to control directly the real and reactive power flow
in the line.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 70


Series compensation:
In series compensation, the FACTS is connected in series with the power system. It works as a controllable

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voltage source. Series inductance occurs in long transmission lines, and when a large current flow causes a large
voltage drop. To compensate, series capacitors are connected.


Shunt compensation:

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Fig 1. Series Compensation

In shunt compensation, power system is connected in shunt (parallel) with the FACTS. It works as a controllable
current source.

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Fig 2. Shunt Compensation
First generation of Facts devices:
1. Static VAR Compensator (SVC)
2. Thyristor-Controlled Series Capacitor (TCSC)

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 71

3. Thyristor-Controlled Phase Shifter (TCPS)
Second generation of Facts devices:
1. Static Compensator (STATCOM)

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2. Static Synchronous Series Compensator (SSSC)
3. Unified Power Flow Controller (UPFC)
Series compensation:
FACTS for series compensation modify line impedance: X is decreased so as to increase the transmittable active
power. However, more reactive power must be provided.

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Shunt compensation:
Reactive current is injected into the line to maintain voltage magnitude. Transmittable active power is increased but
more reactive power is to be provided.

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Simulink block diagram:
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 72

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Output:


Result:
Thus, simulation of facts device in order to control the reactive power flow in a line for efficient operation of the

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power system and transmission network were obtained using MATLAB/simulink.
FirstRanker.com - FirstRanker's Choice
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 1

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?

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DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING

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EE 6711- POWER SYSTEM SIMULATION LABORATORY

VII SEMESTER - R 2013

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Name :
Register No. :
Class :

LABORATORY MANUAL

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 2

VISION
VISION

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is committed to provide highly disciplined, conscientious and
enterprising professionals conforming to global standards through value based quality education and training.

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? To provide competent technical manpower capable of meeting requirements of the industry

? To contribute to the promotion of Academic Excellence in pursuit of Technical Education at different levels

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? To train the students to sell his brawn and brain to the highest bidder but to never put a price tag on heart and
soul


DEPARTMENT OF ELECTRICAL AND ELECTRONICS

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ENGINEERING
To impart professional education integrated with human values to the younger generation, so as to shape
them as proficient and dedicated engineers, capable of providing comprehensive solutions to the challenges in
deploying technology for the service of humanity

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? To educate the students with the state-of-art technologies to meet the growing challenges of the electronics
industry
? To carry out research through continuous interaction with research institutes and industry, on advances in
communication systems

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? To provide the students with strong ground rules to facilitate them for systematic learning, innovation and
ethical practices
MISSION
MISSION
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 3

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PROGRAMME EDUCATIONAL OBJECTIVES (PEOs)
1. Fundamentals
To provide students with a solid foundation in Mathematics, Science and fundamentals of engineering,
enabling them to apply, to find solutions for engineering problems and use this knowledge to acquire higher

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education
2. Core Competence
To train the students in Electrical and Electronics technologies so that they apply their knowledge and
training to compare, and to analyze various engineering industrial problems to find solutions
3. Breadth

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To provide relevant training and experience to bridge the gap between theory and practice which enables
them to find solutions for the real time problems in industry, and to design products
4. Professionalism
To inculcate professional and effective communication skills, leadership qualities and team spirit in the
students to make them multi-faceted personalities and develop their ability to relate engineering issues to

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broader social context
5. Lifelong Learning/Ethics
To demonstrate and practice ethical and professional responsibilities in the industry and society in the large,
through commitment and lifelong learning needed for successful professional career

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PROGRAMME OUTCOMES (POs)
a. To demonstrate and apply knowledge of Mathematics, Science and engineering fundamentals in Electrical
and Electronics Engineering field
b. To design a component, a system or a process to meet the specific needs within the realistic constraints
such as economics, environment, ethics, health, safety and manufacturability

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c. To demonstrate the competency to use software tools for computation, simulation and testing of electrical
and electronics engineering circuits
d. To identify, formulate and solve electrical and electronics engineering problems
e. To demonstrate an ability to visualize and work on laboratory and multidisciplinary tasks
f. To function as a member or a leader in multidisciplinary activities

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g. To communicate in verbal and written form with fellow engineers and society at large
h. To understand the impact of Electrical and Electronics Engineering in the society and demonstrate
awareness of contemporary issues and commitment to give solutions exhibiting social responsibility
i. To demonstrate professional & ethical responsibilities
j. To exhibit confidence in self-education and ability for lifelong learning

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k. To participate and succeed in competitive exams
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 4

COURSE OBJECTIVES
COURSE OUTCOMES

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EE6711 ? POWER SYSTEM SIMULATION LABORATORY
SYLLABUS

To provide better understanding of power system analysis through digital simulation.
LIST OF EXPERIMENTS:

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1. Computation of Parameters and Modeling of Transmission Lines
2. Formation of Bus Admittance and Impedance Matrices and Solution of Networks
3. Load Flow Analysis - I Solution of load flow and related problems using Gauss- Seidel Method.
4. Load Flow Analysis - II: Solution of load flow and related problems using Newton Raphson.
5. Fault Analysis

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6. Transient and Small Signal Stability Analysis: Single-Machine Infinite Bus System
7. Transient Stability Analysis of Multi machine Power Systems
8. Electromagnetic Transients in Power Systems
9. Load ?Frequency Dynamics of Single- Area and Two-Area Power Systems
10. Economic Dispatch in Power Systems.

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1. Ability to understand the concept of MATLAB programming in solving power systems problems.
2. Ability to understand the concept of MATLAB programming in solving parameters of transmission lines.
3. Ability to understand the concept of MATLAB programming in solving medium transmission line parameters.

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4. Ability to understand the concept of MATLAB programming in formation of bus admittance and impedance
matrices.
5. Ability to understand the concept of MATLAB / simulink modeling of single area system.
6. Ability to understand the concept of MATLAB / simulink modeling of two area system.
7. Ability to understand the concept of MATLAB programming in analyzing transient and small signal stability

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analysis of SMIB system.
8. Ability to understand the concept of MATLAB programming in solving economic dispatch in power systems.
9. Ability to understand the concept of MATLAB Programming in analyzing transient stability analysis of multi
machine infinite bus system.
10. Ability to understand the concept of MATLAB programming in solving power flow analysis using Gauss

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siedel method.
11. Ability to understand the concept of MATLAB programming in solving power flow analysis using Newton
Raphson method.
12. Ability to understand the concept of MATLAB programming in solving fault analysis in power system.
13. Ability to understand the concept of MATLAB programming in analyzing transient stability analysis of multi

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machine power systems.
14. Ability to understand the concept of MATLAB / Simulink modeling of FACTS devices.
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EE6711 ? POWER SYSTEM SIMULATION LABORATORY

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CONTENTS
Sl. No. Name of the experiment Page No.
CYCLE 1 EXPERIMENTS
1 Introduction to MATLAB 05
2 Computation of transmission line parameters 13

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3 Modeling of transmission line parameters 19
4 Formation of bus admittance and impedance matrices 21
5 Load frequency dynamics of single area system 26
6 Load frequency dynamics of two area system 29
7 Transient and small signal stability analysis of single machine infinite bus system 32

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CYCLE 2 EXPERIMENTS
8 Economic dispatch in power systems using MATLAB 35
9 Transient Stability Analysis of Multi machine Infinite bus system 41
10 Solution of power flow using Gauss Seidel method. 44
11 Solution of power flow using Newton Raphson method 50

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12 Fault analysis in power system 58
Mini Project
13 Modeling of FACTS devices using SIMULINK 68
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Expt. No.1: INTRODUCTION TO MATLAB
Aim:
To procure sufficient knowledge in MATLAB to solve the power system Problems
Software required:
MATLAB

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Theory:
1. Introduction to MATLAB:
MATLAB is a high performance language for technical computing. It integrates computation, visualization and
programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical
notation. MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary

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tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and
communication theory. MATLAB comprising lot of optional tool boxes and block set like control system, optimization,
and power system and so on.
1.1 Typical uses:
? Mathematics tools and computation

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? Algorithm development
? Modeling, simulation and prototype
? Data analysis, exploration and visualization
? Scientific and engineering graphics
? Application development, including graphical user interface building

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MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical
manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even
for studying and simulating actual power system and electrical system in general. The original concept of a small
and handy tool has evolved replace and/or enhance the usage of traditional simulation tool for advanced engineering
applications.to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes

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1.2 Getting started with MATLAB:
To open the MATLAB applications double click the MATLAB icon on the desktop. To quit from MATLAB type?
>> quit
(Or)
>>exit

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To select the (default) current directory click ON the icon [?] and browse for the folder named ?D:\SIMULAB\xxx?,
where xxx represents roll number of the individual candidate in which a folder should be created already.

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When you start MATLAB you are presented with a window from which you can enter commands interactively.
Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will
probably do a little of both. One good approach is to incrementally create your file of commands by first executing
them.
M-files can be classified into following 2 categories,

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i) Script M-files ? Main file contains commands and from which functions can also be
called
ii) Function M-files ? Function file that contains function command at the first line of the

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M-file
M-files to be created should be placed in your default directory. The M-files developed can be loaded into the work
space by just typing the M-file name.To load and run a M-file named ?ybus.m? in the workspace
>> ybus
These M-files of commands must be given the file extension of ?.m?. However M-files are not limited to being a

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series of commands that you don?t want to type at the MATLAB window, they can also be used to create user defined
function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created
to perform a special type of analysis like control system design and power system analysis. One of the more
generally useful MATLAB tool boxes is simulink ? a drag and-drop dynamic system simulation environment. This will
be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD)

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methodology that is used.
>> Simulink
At the MATLAB prompt type simulink and brings up the ?Simulink Library Browser?. Each of the items in the
Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model
of your own creation. The ?simulink? pallete contains the majority of the elements used in the MATLAB. Simulink

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has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic
equations of your system into simulink in four ways.
1 Using integrators
2. Using transfer functions
3. Using state space equations

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4. Using S- functions (the most versatile approach)
Once you have the dynamics in place you can apply inputs from the ?sources? palettes and look at the results in
the ?sinks? palette. Finally, the most important MATLAB feature is help. At the MATLAB Prompt simply typing

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helpdesk gives you access to searchable help as well as all the MATLAB manuals.
>> helpdesk
To get the details about the command name sqrt, just type?
>> help sqrt
(like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual

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commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common
data types you may see are,
1) arrays 2) strings 3) structures Where sqrt is the command name and you will get pretty good description in
the MATLAB window as follows.
/SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not

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positive.
1.3 MATLAB workspace:
The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the
workspace is to type whos. This command shows you all the variables that are currently in workspace. You should
always change working directory to an appropriate location under your user name.Another useful workspace like

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command is
>>clear all
It eliminates all the variables in your workspace. For example, start MATLAB and execute the following sequence
of commands
>>a=2;

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>>b=5;
>>whos
>>clear all
The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5
respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy

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in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands
and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow
until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere. Finally any
DOS command can be entered in MATLAB as long as it is preceded by any exclamation mark.
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1.3 MATLAB data types:
The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors As for as MATLAB is
concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.
>>a=4.2:

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>>A=[1 4;6 3];
>>whos
Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are
considered arrays. Now let?s look at the content of A and a.
>>a

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>>A
Again two things are important from this example. First anybody can examine the contents of any variables simply
by typing its name at the MATLAB prompt. When typing in a matrix space between elements separate columns,
whereas semicolon separate rows. For practice, create the matrix in your workspace by typing it in all the MATLAB
prompt.

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>>B= [3 0 -1; 4 4 2;7 2 11];
(use semicolon(;) to represent the end of a row)
>>B
Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0
seconds and go up to 5 seconds by increments of 0.001

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>>mytime =0:0.001:5;
Automatic construction of arrays of all ones can also be created as follows,
>>myone=ones (3,2)
1.4 Scalar versus array mathematical operation:
Since MATLAB treats everything as an array, you can add matrices as easily as scalars.

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Example:
>>clear all
>> a=4;
>> A=7;
>>alpha=a+A;

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>>b= [1 2; 3 4];
>>B= [6 5; 3 1];
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>>beta=b+B

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The violation of the rules in matrix algebra can be understood by the following example.
>>clear all
>>b=[1 2;3 4];
>>B=[6 7];
>>beta=b*B

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In contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another,
element by element. The typical scalar commands are used for this ?+,-,/, *, ^? except you put a ?.? in front of the
scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just
>> [1 2 3 4].*[6 7 8 9]
1.6 Conditional statements :

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Like most programming languages, MATLAB supports a variety of conditional statements and looping statements.
To explore these simply type
>>help if
>>help for
>>help while

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Example :

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]Looping :

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>>if z=0
>>y=0
>>else
>>y=1/z

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>>end


>>for n=1:2:10
>>s=s+n^2

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>>end
- Yields the sum of 1^2+3^2+5^2+7^2+9^2
1.7 Plotting:
MATLAB?s potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of
commands you can have quite a bit of capability.

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Graphs can be plotted and can be saved in different formulas.
>> clear all
>> t=0:10:360;

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>> y=sin (pi/180 * t);
To see a plot of y versus t simply type,
>> plot(t,y)
To add a label, legend, grid and title use
>> xlabel (?Time in sec?);

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>>ylabel (?Voltage in volts?)
>>title (?Sinusoidal O/P?);
>>legend (?Signal?);
The commands above provide the most plotting capability and represent several shortcuts to the low-level
approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a

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pdf manual on handle graphics for those really interested in it.
1.8 Functions:
As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The
commands and functions that comprise the new function must be put in a file whose name defines the name of the
new function, with a filename extension of '.m'. A function is a generalized input/output device. We can give some

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input arguments and provides some output. MATLAB functions allow us much capability to expand MATLAB?s
usefulness. We will start by looking at the help on functions :
>>help function
We will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of
given impedance matrix(z)?

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z= [5 2 4;
1 4 5] as input, the output would be,


y= [0.2 0.5 0.25;

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1 0.25 0.2] which is the reciprocal of each elements.
To perform the same name the function ?admin? and noted that ?admin? must be stored in a function M-file named
?admin.m?. Using an editor, type the following commands and save as ?admin.m?.
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function y = admin(z)
y = 1./z
return
Simply call the function admin from the workspace as follows,
>>z=[5 2 4;

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1 4 5]
>>admin(z)
The output will be,
ans = 0.2 0.5 0.25
1 0.25 0.2

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Otherwise the same function can be called for any times from any script file provided the function M-file is available
in the current directory. With this introduction anybody can start programming in MATLAB and can be updated
themselves by using various commands and functions available. Concerned with the ?Power System Simulation
Laboratory?, initially solve the Power System Problems manually, list the expressions used in the problem and then
build your own MATLAB program or function.

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Result:
Thus, the sufficient knowledge about MATLAB to solve power system problems were obtained.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving power
systems problems.

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Application:
MATLAB Used
Algorithm development
Scientific and engineering graphics

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Modeling, simulation, and prototyping
Application development, including Graphical User Interface building
Math and computation
Data analysis, exploration, and visualization

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1. What is meant by MATLAB?
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming

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in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
2. What are the different functions used in MATLAB?
The different function intersect , bitshift, categorical, isfield
3. What are the different operators used in MATLAB?
Arithmetic, Relational Operations, Logical Operations, Set Operations, Bit-Wise Operations

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4. What are the different looping statements used in MATLAB?
For , while
5. What are the different conditional statements used in MATLAB?
If, else
6. What is Simulink?

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Simulink, developed by Math Works, is a graphical programming environment for modeling, simulating and analyzing multi
domain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block
libraries.
7. What are the four basic functions to solve Ordinary Differential Equations (ODE)?
ode45, ode15s, ode15i

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8. Explain how polynomials can be represented in MATLAB?
poly, polyval, polyvalm , roots
9. What is meant by M-file?
An m-file, or script file, is a simple text file where you can place MATLAB commands. When the file is run, MATLAB reads
the commands and executes them exactly as it would if you had typed each command sequentially at the MATLAB prompt.

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10. What is Interpolation and Extrapolation in MATLAB?
Interpolation in MATLAB

is divided into techniques for data points on a grid and scattered data points.
11. List out some of the common toolboxes present in MATLAB?

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Control system tool box, power system tool box, communication tool box,
12. What are the MATLAB System Parts?
MATLAB Language, MATLAB working environment, Graphics handler, MATLAB mathematical library, MATLAB Application
Program Interface.
13. What are the different applications of MATLAB?

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Algorithm development, Scientific and engineering graphics, Modeling, simulation, and prototyping, Application
development, including Graphical User Interface building, Math and computation,Data analysis, exploration, and
visualization

Viva - voce

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 14

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Aim:
Expt.No.2: COMPUTATION OF TRANSMISSION LINES
PARAMETERS

To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and

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double circuit transmission lines for different conductor arrangements
Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The

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inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The
resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Algorithm:
Step 1: Start the Program

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Step 2: Get the input values for distance between the conductors and bundle spacing of
D 12, D 23 and D 13
Step 3: From the formula given calculate GMD
GMD= (D 12* D 23*D 13)
1/3

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Step 4: Calculate the Value of Impedance and Capacitance of the line
Step 5: End the Program
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results
Exercise:1

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A three phase transposed line has its conductors placed at a distance of 11 m, 11 m & 22 m. The conductors have
a diameter of 3.625cm Calculate the inductance and capacitance of the transposed conductors.
(a) Determine the inductance and capacitance per phase per kilometer of the above three lines.
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(b) Verify the results using the MATLAB program.
Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km

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Where,
D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D

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GMR = r' = 0.7788 r
Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &

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GMR r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Program:
%3 phase single circuit
D12=input('enter the distance between D12in cm: ');
D23=input('enter the distance between D23in cm: ');
D31=input('enter the distance between D31in cm: ');

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d=input('enter the value of d: ');
r=d/2;
Ds=0.7788*r;
x=D12*D23*D31;
Deq=nthroot(x,3);

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Y=log(Deq/Ds);
inductance=0.2*Y
capacitance=0.0556/(log(Deq/r))

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fprintf('\n The inductance per phase per km is %f mH/ph/km \n',inductance);
fprintf('\n The capacitance per phase per km is %f mf/ph/km \n',capacitance);
Output:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km

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Exercise:2
A 345 kV double-circuit three-phase transposed line is composed of two AC SR, 1,431,000-cmil, 45/7 bobolink
conductors per phase with vertical conductor configuration as show in figure. The conductors have a diameter of
1.427 inch and a GMR of 0.564 inch. The bundle spacing in 18 inch. Find the inductance and capacitance per phase
per Kilometer of the line.

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Calculation:
Inductance:
The general formula:
L = 0.2 ln (D m / D s) mH / Km
Where,

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D m = geometric mean distance (GMD)
D s = geometric mean radius (GMR)
Single phase 2 wire system:
GMD = D
GMR = r' = 0.7788 r

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Where, r is the radius of conductor
Three phase ? symmetrical spacing :
GMD = D GMR = re-1/4 = r'
Where, r = radius of conductor &
GMR r' = 0.7788 r

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Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km

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Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various
cases.
Program:
%3 phase double circuit
%3 phase double circuit

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S = input('Enter row vector [S11, S22, S33] = ');
H = input('Enter row vector [H12, H23] = ');
d = input('Bundle spacing in inch = ');
dia = input('Conductor diameter in inch = '); r=dia/2;
Ds = input('Geometric Mean Radius in inch = ');

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S11 = S(1); S22 = S(2); S33 = S(3); H12 = H(1); H23 = H(2);
a1 = -S11/2 + j*H12;
b1 = -S22/2 + j*0;
c1 = -S33/2 - j*H23;
a2 = S11/2 + j*H12;

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b2 = S22/2 + j*0;
c2 = S33/2 - j*H23;
Da1b1 = abs(a1 - b1); Da1b2 = abs(a1 - b2);
Da1c1 = abs(a1 - c1); Da1c2 = abs(a1 - c2);
Db1c1 = abs(b1 - c1); Db1c2 = abs(b1 - c2);

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Da2b1 = abs(a2 - b1); Da2b2 = abs(a2 - b2);
Da2c1 = abs(a2 - c1); Da2c2 = abs(a2 - c2);
Db2c1 = abs(b2 - c1); Db2c2 = abs(b2 - c2);
Da1a2 = abs(a1 - a2);
Db1b2 = abs(b1 - b2);

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Dc1c2 = abs(c1 - c2);
DAB=(Da1b1*Da1b2* Da2b1*Da2b2)^0.25;
DBC=(Db1c1*Db1c2*Db2c1*Db2c2)^.25;
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DCA=(Da1c1*Da1c2*Da2c1*Da2c2)^.25;
GMD=(DAB*DBC*DCA)^(1/3)
Ds = 2.54*Ds/100; r = 2.54*r/100; d = 2.54*d/100;
Dsb = (d*Ds)^(1/2); rb = (d*r)^(1/2);
DSA=sqrt(Dsb*Da1a2); rA = sqrt(rb*Da1a2);

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DSB=sqrt(Dsb*Db1b2); rB = sqrt(rb*Db1b2);
DSC=sqrt(Dsb*Dc1c2); rC = sqrt(rb*Dc1c2);
GMRL=(DSA*DSB*DSC)^(1/3)
GMRC = (rA*rB*rC)^(1/3)
L=0.2*log(GMD/GMRL) % mH/km

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C = 0.0556/log(GMD/GMRC) % micro F/km
Output of the program:
The inductance per phase per km is 1.377882 mH/ph/km
The capacitance per phase per km is 0.008374 mf/ph/km
Result:

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Thus, the positive sequence line parameters L and C per phase per kilometer of a three phase single and double
circuit transmission lines for different conductor arrangements were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving
parameters of transmission lines.

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Application :
It is used in transmission and distribution of electrical power system.
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1. What is meant by geometric mean distance?
GMD stands for Geometrical Mean Distance. It is the equivalent distance between conductors. GMD comes into picture
when there are two or more conductors per phase used as in bundled conductors.

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2. What is meant by geometric mean radius?
GMR stands for Geometric mean Radius. GMR is calculated for each phase separately
3. What is meant by transposition of lines?
transposition of transmission line is to rotate the conductors which result in the conductor or a phase being moved to next
physical location in a regular sequence. Purpose of Transpostion. The transposition arrangement of high voltage lines

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also helps to reduce the system power loss.
4. What is meant by bundling of conductors?
Mostly long distance power lines are either 220 kV or 400 kV, avoidance of the occurrence of corona is desirable. The
high voltage surface gradient is reduced considerably by having two or more conductors per phase in close proximity.
This is called Conductor bundling

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5. What is meant by double circuit line?
A double-circuit transmission line has two circuits. For three-phase systems, each tower supports and insulates six
conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits.
6. What is meant by ACSR conductor?
Aluminium conductor steel-reinforced cable (ACSR) is a type of high-capacity, high-strength stranded conductor typically

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used in overhead power lines. The outer strands are high-purity aluminium, chosen for its good conductivity, low weight
and low cost
7. List out the advantages of bundled conductors.
Bundled conductors are primarily employed to reduce the corona loss and radio interference. However they have several
advantages: Bundled conductors per phase reduces the voltage gradient in the vicinity of the line.

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8. What is meant by symmetrical spacing?
9. What is meant by skin effect?
Skin effect is a tendency for alternating current (AC) to flow mostly near the outer surface of an electrical conductor, such
as metal wire. The effect becomes more and more apparent as the frequency increases.
10. What is meant by proximity effect?

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When the conductors carry the high alternating voltage then the currents are non-uniformly distributed on the cross-
section area of the conductor. This effect is called proximity effect. The proximity effect results in the increment of the
apparent resistance of the conductor due to the presence of the other conductors carrying current in its vicinity.
11. What is meant by Ferranti effect?
In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission

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line, above the voltage at the sending end. This occurs when the line is energized, but there is a very light load or the load
is disconnected.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 20

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Expt.No.3: MODELING OF TRANSMISSION LINE
PARAMETERS

Aim:
To perform the modeling and performance of medium transmission lines

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Software required:
MATLAB 7.6
Theory:
Transmission line has four parameters namely resistance, inductance, capacitance and conductance. The
inductance and capacitance are due to the effect of magnetic and electric fields around the conductor. The

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resistance of the conductor is best determined from the manufactures data, the inductances and capacitances can
be evaluated using the formula.
Formula used:
Inductance:
The general formula:

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L = 0.2 ln (D m / D s) mH / Km
Where,
D m = geometric mean distance (GMD)
Ds = geometric mean radius (GMR)
Single phase 2 wire system:

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GMD = D
GMR = re-1/4 = r' = 0.7788 r
Where r is called the radius of conductor
Three phase ? symmetrical spacing:
GMD = D GMR = re-1/4 = r'

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Where, r = radius of conductor & GMR = re-1/4 = r' = 0.7788 r
Capacitance:
A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by,
C = 0.0556/ ln (Deq / r) ?F/km
Where, GMD is the ?Geometric mean distance? which is same as that defined for inductance under various cases.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 21

Algorithm:
Step 1: Start the Program.
Step 2: Get the input values for conductors.

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Step 3: To find the admittance (y) and impedance (z).
Step 4: To find receiving end voltage and receiving end power.
Step 5: To find receiving end current and sending end voltage and current.
Step 6: To find the power factor and sending ending power and regulation.
Procedure:

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1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.
4. Execute the program by either pressing Tools ? Run.
5. View the results

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Result:
Thus, the modeling and performance of medium transmission lines were obtained using MATLAB.
Outcome:
By doing the experiment, the students can understand the concepts of MATLAB programming in solving medium
transmission line parameters.

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Application
It is used in transmission and distribution of electrical power system.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 22

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1. What is meant by regulation?
Regulation is the ratio of no load to full load and no load

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2. What are the different types of transmission line?
Single circuit
Double circuit
3. What is meant by efficiency of transmission line?
Transmission line efficiency is the ratio of receiving end power to sending end power.

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4. What is meant by nominal ? method?
The transmission line analysis with inductor and capacitor arrange in ? model.
5. What is meant by nominal T method?
The transmission line analysis with inductor and capacitor arrange in T model.
6. What is the need for different transmission line models?

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1. Nominal ?
2. Nominal T
7. What is meant by surge impedance?

The capacity to withstand the transmission line loading.

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 23

Expt.No.4: FORMATION OF BUS ADMITTANCE AND
IMPEDANCE MATRICES

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Aim:
To determine the bus admittance and impedance matrices for the given power system network
Software required:
MATLAB 7.6

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Theory:
Formation of Y
bus
matrix:
Y-bus may be formed by inspection method only if there is no mutual coupling between the lines. Every

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transmission line should be represented by ?- equivalent. Shunt impedances are added to diagonal element
corresponding to the buses at which these are connected. The off diagonal elements are unaffected. The equivalent
circuit of Tap changing transformers is included while forming Y-bus matrix.
Formation of Z
bus

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matrix:
In bus impedance matrix the elements on the main diagonal are called driving point impedance and the off-
diagonal elements are called the transfer impedance of the buses or nodes. The bus impedance matrix is very useful
in fault analysis.
The bus impedance matrix can be determined by two methods. In one method we can form the bus admittance

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matrix and than taking its inverse to get the bus impedance matrix. In another method, the bus impedance matrix can
be directly formed from the reactance diagram and this method requires the knowledge of the modifications of
existing bus impedance matrix due to addition of new bus or addition of a new line (or impedance) between existing
buses.
Algorithm:

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Step 1: Start the program.
Step 2: Enter the bus data matrix in command window.
Step 3: Calculate the values:
Y=y bus (busdata)
Y= y bus (z)

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Z bus = inv(Y)
Step 4: Form the admittance Y bus matrix.
Step 5: Form the Impedance Z bus matrix.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 24

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Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program in the editor window.

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4. Execute the program by pressing Tools ? Run.
5. View the results.
Exercise:
(i) Determine the Y bus matrix for the power system network shown in fig.
(ii) Check the results obtained in using MATLAB.

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2. (i) Determine Z bus matrix for the power system network shown in fig.

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(ii) Check the results obtained using MATLAB.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 25

Line data:

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From To R X B/2

Bus Bus
1 2 0.10 0.20 0.02

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1 4 0.05 0.20 0.02
1 5 0.08 0.30 0.03
2 3 0.05 0.25 0.03
2 4 0.05 0.10 0.01
2 5 0.10 0.30 0.02

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2 6 0.07 0.20 0.025
3 5 0.12 0.26 0.025
3 6 0.02 0.10 0.01
4 5 0.20 0.40 0.04
5 6 0.10 0.30 0.03

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Program:
% Program to form Admittance and Impedance Bus Formation....
clc
fprintf('FORMATION OF BUS ADMITTANCE AND IMPEDANCE MATRIX\n\n')

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fprintf('Enter linedata in order of from bus,to bus,r,x,b\n\n')
linedata = input('Enter line data : ');
fb = linedata(:,1); % From bus number...
tb = linedata(:,2); % To bus number...
r = linedata(:,3); % Resistance, R...

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x = linedata(:,4); % Reactance, X...
b = linedata(:,5); % Ground Admittance, B/2...
z = r + i*x; % Z matrix...
y = 1./z; % To get inverse of each element...
b = i*b; % Make B imaginary...

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nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches...
ybus = zeros(nbus,nbus); % Initialise YBus...
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 26

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% Formation of the Off Diagonal Elements...
for k=1:nbranch
ybus(fb(k),tb(k)) = -y(k);
ybus(tb(k),fb(k)) = ybus(fb(k),tb(k));
end

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% Formation of Diagonal Elements....
for m=1:nbus
for n=1:nbranch
if fb(n) == m | tb(n) == m
ybus(m,m) = ybus(m,m) + y(n) + b(n);

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end
end
end
ybus = ybus % Bus Admittance Matrix
zbus = inv(ybus); % Bus Impedance Matrix

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zbus
Result:
Thus, the bus admittance and impedance matrices for the given power system network were obtained using
MATLAB.
Outcome:

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By doing the experiment, the students can understand the concepts of MATLAB programming in solving bus
admittance and impedance matrix.

Application:
Bus admittance matrix is used for load flow analysis

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Bus impedance matrix is used to short circuit study
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 27


1. What is meant by singular transformation method?

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The matrix formed by graph theory.
2. What is meant by inspection method?
The admittance matrix calculated directly is called inspection method.
3. What is meant by bus?
Bus is junction point of transmission line.

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4. What are the components of a power system?
Generator, Transformer, transmission line, load
5. What is meant by single line diagram?
Power system represented in simple graphical view
6. How are the loads represented in reactance or impedance diagram?

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loads represented in reactance diagram resistor with reactor.
7. What are the different methods to solve bus admittance matrix?
Inspection method, direct method
8. What are the elements of the bus admittance matrix?
Reactance

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9. What are the elements of the bus impedance matrix?
Resistor and reactor
10. What are the methods available for forming bus impedance matrix?
1. Bus building algorithm
2. using y bus

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11. Define per unit value.
Per unit is defined as the ratio of actual value to base value
12. What are the advantages of per unit computations?

The manufacture is used as common value

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It is easy to understand.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 28

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Expt. No. 5: LOAD FREQUENCY DYNAMICS OF SINGLE AREA
POWER SYSTEM
Aim:
To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a single area power
system with and without load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality of power
supply. A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor
systems) of the system leading to change in system frequency. The speed change form synchronous speed initiates
the governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units.
Procedure:
1. Enter the command window of the MATLAB.
2. Create a new Model by selecting File - New ? Model.
3. Pick up the blocks from the simulink library browser and form a block diagram.

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4. After forming the block diagram, save the block diagram.
5. Double click the scope and view the result.
Exercise:
1. An isolated power station has the following parameters:
Turbine time constant, ? T = 0.5sec, Governor time constant, ? g = 0.2sec

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Generator inertia constant, H = 5sec, Governor speed regulation = R per unit
The load varies by 0.8 percent for a 1 percent change in frequency, i.e, D = 0.8
(a) Use the Routh ? Hurwitz array to find the range of R for control system stability.
(b) Use MATLAB to obtain the root locus plot.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 29

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(c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250MW at nominal
frequency of 60Hz. A sudden load change of 50 MW (?P L = 0.2 per unit) occurs.
(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.

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Without integral controller: (simulink block diagram)

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With integral controller: (simulink block diagram)

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Exercise: 1
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping
co efficient 0.016 PU MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2 s,

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 30

Viva - voce
Load change 60 MW, The load varies by 0.8 percent for a 1 percent change in frequency, Determine the steady
state frequency deviation in Hz

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(i) Find the steady state frequency deviation in Hz.
(ii) Use MATLAB to obtain the time domain performance specifications and the frequency deviation step response.
Exercise: 2
An isolated power system has the following parameter:
Turbine rated output 300 MW, Nominal frequency 50 Hz, Governer speed regulation 2.5 Hz per unit MW, Damping

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co efficient 0.016 p.u. MW / Hz, Inertia constant 5 sec, Turbine time constant 0.5 sec, Governer time constant 0.2
sec, Load change 60 MW, The system is equipped with secondary integral control loop and the integral controller
gain is K f = 1. Obtain the frequency deviation for a step response
Result:
Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a single area power system with

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and without load frequency controllers (LFC) were obtained using MATLAB/ simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a single area power system with and without load frequency controllers (LFC) using MATLAB/Simulink
Application:

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To maintain the power and frequency constant in electrical power system.


1. What is meant by single area system?
If the generation system is considering only one generation unit and one load area it can be treated as a single area system

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2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency
constant
3. What is meant by automatic generation control?
In an electric power system, automatic generation control (AGC) is a system for adjusting the power output of multiple

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generators at different power plants, in response to changes in the load
4. What is meant by speed regulation?
Speed regulation is no load speed to full load speed and no load speed.
5. What is meant by inertia constant?
Inertia constant is ?the ratio of kinetic energy of a rotor of a synchronous machine to the rating of a machine

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 31

6. What are the major control loops used in large generators?
Primary control loop
Secondary control loop

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7. What is the use of secondary loop?
Secondary control loop is used to maintain the frequency as constant.
8. What is the advantage of AVR loop over ALFC loop?

AVR loop is much faster than the ALFC loop and therefore there is a tendency, for the

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AVR dynamics to settle down before they can make themselves felt in the slower load ?
frequency control channel.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 32

Expt.No.6: LOAD FREQUENCY DYNAMICS OF TWO AREA

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POWER SYSTEM
Aim:

To become familiar with modeling and analysis of the frequency and tie-line flow dynamics of a two area power
system without and with load frequency controllers (LFC) and to design better controllers for getting better responses

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Software required:
MATLAB / SIMULINK
Theory:
Active power control is one of the important control actions to be performed in the normal operation of the system
to match the system generation with the continuously changing system load in order to maintain the constancy of

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system frequency to a fine tolerance level. This is one of the foremost requirements in proving quality power supply.
A change in system load causes a change in the speed of all rotating masses (Turbine ? generator rotor systems) of
the system leading to change in system frequency. The speed change form synchronous speed initiates the
governor control (primary control) action result in the entire participating generator ? turbine units taking up the
change in load, stabilizing system frequency. Restoration of frequency to nominal value requires secondary control

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action which adjusts the load - reference set points of selected (regulating) generator ? turbine units
Procedure:
1. Enter the command window of the MATLAB
2. Create a new model by selecting File - New ? Model
3. Pick up the blocks from the simulink library browser and form a block diagram

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4. After forming the block diagram, save the block diagram
5. Double click the scope and view the result
Exercise:
A Two- area system connected by a tie- line has the following parameters on a 1000 MVA common base.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 33

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Area 1 2
Speed regulation R 1=0.05 R 2=0.0625
damping coefficient D 1=0.6 D 2=0.9
Inertia constant H 1=5 H 2=4

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Base power 1000MVA 1000MVA
Governor time constant ? g1 = 0.2sec ? g1 = 0.3sec
Turbine time constant ? T1 =0.5sec ? T1 =0.6sec
The units are operating in parallel at the nominal frequency of 60Hz. The synchronizing power coefficient is
computed from the initial operating condition and is given to be P s = 2 p.u. A load change of 187.5 MW occurs in

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area1.
(a) Determine the new steady state frequency and the change in the tie-line flow.
(b) Construct the SIMULINK block diagram and obtain the frequency deviation response for the condition in part (a).
Simulink block diagram:

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Result:

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Thus, the modeling and analysis of the frequency and tie-line flow dynamics of a two area power system with and
without load frequency controllers (LFC) were obtained using MATLAB / Simulink.
Outcome:
By doing the experiment, the students can understand the modeling and analysis of the frequency and tie-line flow
dynamics of a two area power system with and without load frequency controllers (LFC) using MATLAB/Simulink.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 34


Application:

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To maintain the power and frequency constant in electrical power system.



1. What is meant by two area system?

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power system is interconnected one where no of generators are connected together and run in unison manner to meet
the demand
2. What is meant by load frequency control?
Load frequency control, as the name signifies, regulates the power flow between different areas while holding the
frequency constant

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3. What is meant by area frequency response coefficient?
a and b
4. What are the major control loops used in large generators?
Frequency control loop
Current control loop

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5. What is the use of secondary loop?

Secondary control loop is used to maintain the frequency as constant.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 35

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Expt.No.7: TRANSIENT AND SMALL SIGNAL STABILITY
ANALYSIS OF SINGLE MACHINE INFINITE BUS
SYSTEM

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Aim:
To become familiar with various aspects of the transient and small signal stability analysis of Single-Machine-
Infinite Bus (SMIB) system
Software required:
MATLAB 7.6

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Theory:
Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power

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balance is upset and the generating units rotors experience either acceleration or deceleration. The system may
come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:

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When a power system is under steady state, normal operating condition, the system may be subjected to small
disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
(a) Steady increase in rotor angle due to lack of synchronizing torque.

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(b) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program

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4. Execute the program by pressing Tools ? Run
5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 36

Exercise:

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A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis transient reactance X d
1
=
0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance?s are
marked on the diagram on a common system base. The generator is delivering real power P e = 0.8 per unit and Q =

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0.074 per unit to the infinite bus at a voltage of V = 1 per unit.

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a) A temporary three-phase fault occurs at the sending end of the line at point F. When the fault is cleared, both
lines are intact. Determine the critical clearing angle and the critical fault clearing time.
b) Verify the result using MATLAB program

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Result:
Thus, the various aspects of the transient and small signal stability analysis of Single-Machine-Infinite Bus (SMIB)
system were analyzed using MATLAB.

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Outcome:
By doing the experiment, the transient and small stability analysis of Single machine Infinite Bus system were
analyzed using MATLAB programming
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 37

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1. What is meant by stability?
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of
operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically

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the entire system remains intact
2. What is meant by transient stability?
The ability of a synchronous power system to return to stable condition and maintain its synchronism following a relatively
large disturbance arising from very general situations like switching ON and OFF of circuit elements, or clearing of faults, etc.
is referred to as the transient stability in power system

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3. What is meant by single machine infinite bus?
The single-machine infinite-bus power system is an approximate representation of a kind of real power systems, where a
power plant with a generator or a group of generators are connected by transmission lines to a very large power network
4. Define ?Fault Clearing Time
The Critical Fault Clearing Time (CFCT) is the most common criteria for evaluation of transient angle stability. The CFCT is

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the maximum time during which a disturbance can be applied without the system losing its stability
5. Write the two ways by which transient stability study can be made in a system where one machine is swinging
with respect to an infinite bus.
6. Define ? Critical Clearing Time
The Critical Clearing Time is the maximum time during which a disturbance can be applied without the system losing its

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stability. The aim of this calculation is to determine the characteristics of protections required by the power system.
7. Define ? Critical Clearing Angle
The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of
synchronism
8. What is meant by Equal Area Criterion?

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The Equal area criterion is a ?graphical technique used to examine the transient stability of the machine systems (one or more
than one) with an infinite bus?
9. Write the power angle equation and draw the power angle curve.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The

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angle between the two is known as the power angle or torque angle
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 38

Expt.No.8: ECONOMIC DISPATCH IN POWER SYSTEMS USING

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MATLAB
Aim:
To understand the fundamentals of economic dispatch and solve the problem using classical method with and
without line losses
Software required:

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MATLAB 7.6
Theory:
Mathematical model for economic dispatch of thermal units without transmission loss:
Statement of economic dispatch problem:
In a power system, with negligible transmission loss and with N number of spinning thermal generating units the

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total system load PD at a particular interval can be met by different sets of generation schedules
{PG 1
(k)
, PG 2
(k)

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, ?PG N
(K)
}; k = 1,2,? .... N S
Out of these N s set of generation schedules, the system operator has to choose the set of schedules, which
minimize the system operating cost, which is essentially the sum of the production cost of all the generating units.

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This economic dispatch problem is mathematically stated as an optimization problem.
Algorithm:
Step 1: Start the program
Step 2: Get the input values of alpha, beta and gamma
Step 3: Use the intermediate variable as lambda

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Step 4: Iterate the variables up to feasible solution
Step 5: To find total cost and economic cost of generator
Step 6: End the program.
Procedure:
1. Enter the command window of the MATLAB.

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2. Create a new M ? file by selecting file - new ? M ? File
3. Type and save the program.
4. Execute the program by either pressing Tools ? Run.
5. View the results.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 39

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Exercise 1:
The fuel cost functions for three thermal plants in $/h are given by
C 1 = 500 + 5.3 P 1 + 0.004 P 1
2;

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P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2;
P 2 in MW
C 3 = 200 +5.8 P 3 + 0.009 P 3

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2
; P 3 in MW
The total load, P D is 800MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost
in $/hr by analytical method. Verify the result using MATLAB program.
Program:

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clc;
clear all;
warning off;
a=[.004; .006; .009];
b=[5.3; 5.5; 5.8];

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c=[500; 400; 200];
Pd=800;
delp=10;
lambda=input('Enter estimated value of lambda=');
fprintf('\n')

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disp(['lambda P1 P1 P3 delta p delta lambda'])
iter=0;
while abs(delp)>=0.001
iter=iter+1;
p=(lambda-b)./(2*a);

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delp=Pd-sum(p);
J=sum(ones(length(a),1)./(2*a));
dellambda=delp/J;
disp([lambda,p(1),p(2),p(3),delp,dellambda])
lambda=lambda+dellambda;

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end
lambda
p
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 40

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totalcost=sum(c+b.*p+a.*p.^2)
Output:
Enter estimated value of lambda= 10
lambda P 1 P 2 P 3 delta p delta lambda
10.0000 587.5000 375.0000 233.3333 -395.8333 -1.5000

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8.5000 400.0000 250.0000 150.0000 0 0
lambda =
8.5000
p =
400.0000

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250.0000
150.0000
Total cost = 6.6825e+003
Exercise 2:
The fuel cost functions for three thermal plants in $/h are given by

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C 1 = 500 + 5.3 P 1 + 0.004 P 1
2
; P 1 in MW
C 2 = 400 + 5.5 P 2 + 0.006 P 2
2

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; P 2 in MW
C 3 = 200 + 5.8 P 3 + 0.009 P 3
2
; P 3 in MW
The total load , P D is 975MW. The generation limits are:

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200 ? P 1 ? 450 MW
150 ? P 2 ? 350 MW
100 ? P 3 ? 225 MW
Find the optimal dispatch and the total cost in $/h by analytical method. Verify the result using MATLAB program.
Program:

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clear
clc
n=3;
demand=925;
a=[.0056 .0045 .0079];

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b=[4.5 5.2 5.8];
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 41

c=[640 580 820];
Pmin=[200 250 125];

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Pmax=[350 450 225];
x=0; y=0;
for i=1:n
x=x+(b(i)/(2*a(i)));
y=y+(1/(2*a(i)));

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lambda=(demand+x)/y
Pgtotal=0;
for i=1:n
Pg(i)=(lambda-b(i))/(2*a(i));
Pgtotal=sum(Pg);

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end
Pg
for i=1:n
if(Pmin(i)<=Pg(i)&&Pg(i)<=Pmax(i));
Pg(i);

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else
if(Pg(i)<=Pmin(i))
Pg(i)=Pmin(i);
else
Pg(i)=Pmax(i);

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end
end
Pgtotal=sum(Pg);
end
Pg

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if Pgtotal~=demand
demandnew=demand-Pg(1)
x1=0;
y1=0;
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 42

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for i=2:n
x1=x1+(b(i)/(2*a(i)));
y1=y1+(1/(2*a(i)));
end

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lambdanew=(demandnew+x1)/y1
for i=2:n
Pg(i)=(lambdanew-b(i))/(2*a(i));
end
end

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end
Pg
Output:
lambda =
8.6149

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Pg =
367.4040 379.4361 178.1598
Pg =
350.0000 379.4361 178.1598
Demand new =

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575
Lambda new =
8.7147
Pg =
350.0000 390.5242 184.4758

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Result:
Thus, the fundamentals of economic dispatch problem using classical method with and without line losses were
obtained using MATLAB.
Outcome:
By doing the experiment, the MATLAB programming for economic dispatch problem has been coded for with and

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without loss conditions.

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 43

Application:

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Used in power system with lowest cost and schedule with generating unit

1. Define ? Economic Dispatch
Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to
meet the system load, at the lowest possible cost, subject to transmission and operational constraints

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2. What is meant by lambda iteration method?
lambda iteration method is used to calculated economic dispatch.
3. Define ? Unit commitment
Unit Commitment (UC) is the problem of determining the schedule of generating units within a power system subject to
device and operating constraints

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4. What are the different constraints in unit commitment?
Fuel constraint, station constraint
5. Compare unit commitment from economic dispatch.
Schedule of power generating unit
Operate with lowest price

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6. What is the objective of economic dispatch problem?
objective of economic dispatch is lowest possible cost, subject to transmission and operational constraints
7. What is meant by incremental cost?
Cost function of economic dspatch
8. What is meant by base point?

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Minimum load Base load in power system
9. What is meant by participation factor?

Participation factors are scalars intended to measure the relative contribution of system modes to system states, and of
system states to system modes, for linear systems

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Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 44

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Aim:
Expt.NO.9: TRANSIENT STABILITY ANALYSIS OF MULTI
MACHINE INFINITE BUS SYSTEM

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To become familiar with various aspects of the transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system
Software required:
MATLAB 7.6
Theory:

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Transient stability:
When a power system is under steady state, the load plus transmission loss equals to the generation in the
system. The generating units run at synchronous speed and system frequency, voltage, current and power flows are
steady. When a large disturbance such as three phase fault, loss of load, loss of generation etc., occurs the power
balance is upset and the generating units rotors experience either acceleration or deceleration. The system may

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come back to a steady state condition maintaining synchronism or it may break into subsystems or one or more
machines may pull out of synchronism. In the former case the system is said to be stable and in the later case it is
said to be unstable.
Small signal stability:
When a power system is under steady state, normal operating condition, the system may be subjected to small

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disturbances such as variation in load and generation, change in field voltage, change in mechanical toque etc., the
nature of system response to small disturbance depends on the operating conditions, the transmission system
strength, types of controllers etc. Instability that may result from small disturbance may be of two forms,
1. Steady increase in rotor angle due to lack of synchronizing torque.
2. Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.

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Procedure:
1. Enter the command window of the MATLAB
2. Create a new M ? file by selecting File - New ? M ? File
3. Type and save the program
4. Execute the program by pressing Tools ? Run

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5. View the results
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 45

Exercise:
1. Transient stability analysis of a 9-bus, 3-machine, 60 Hz power system with the following system

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modelling requirements:
I. Classical model for all synchronous machines, models for excitation and speed governing systems not
included.
(a) Simulate a three-phase fault at the end of the line from bus 5 to bus 7 near bus 7 at time = 0.0 sec.
Assume that the fault is cleared successfully by opening the line 5-7 after 5 cycles ( 0.083 sec) . Observe the system

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for 2.0 seconds
(b) Obtain the following time domain plots:
- Relative angles of machines 2 and 3 with respect to machine 1
- Angular speed deviations of machines 1, 2 and 3 from synchronous speed
- Active power variation of machines 1, 2 and 3.

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(c) Determine the critical clearing time by progressively increasing the fault clearing time.

Program:
For (a)
Pm = 0.8; E = 1.17; V = 1.0;

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X1 = 0.65; X2 = inf; X3 = 0.65;
eacfault (Pm, E, V, X1, X2, X3)
For( b)
Pm = 0.8; E = 1.17; V = 1.0;
X1 = 0.65; X2 = 1.8; X3 = 0.8;

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eacfault (Pm, E, V, X1, X2, X3)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 46

Viva - voce
Result:

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Thus, the various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB) system were obtained
using MATLAB.
Outcome:
By doing the experiment, various aspects of transient stability analysis of Multi -Machine-Infinite Bus (MMIB)
system were obtained using MATLAB programming

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Application:
Used to analysis to transient and steady state behavior of generator.

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1. What is meant by steady state stability?
power system stability as the ability of the power system to return to steady state without losing synchronism.
2. What is meant by small signal stability?
Small-signal stability analysis is about power system stability when subject to small disturbances
3. Write the swing equation in a power system.

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4. Define ? Swing Curve
The swing curve is the plot between the power angle and time. It is usually plotted for a transient state to study the nature of
variation in angle for a sudden large disturbances
5. Write the simplified power angle equation and the expression for P max.

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6. Define ? Power Angle
Power angle is the angle between voltage and current, so theoretically it can be defined wherever voltage and current exists

Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 47

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Expt.No.10: SOLUTION OF POWER FLOW USING GAUSS-
SEIDEL METHOD
Aim:
To understand, in particular, the mathematical formulation of power flow model in complex form and a simple

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method of solving power flow problems of small sized system using Gauss-Seidel iterative algorithm
Software required:
MATLAB 7.6
Theory:
The Gauss Siedel method is an iterative algorithm for solving a set of non-linear load flow equations. Power-flow

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or load-flow studies are important for planning future expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained from the power-flow study is the magnitude and
phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power
systems are usually too complex to allow for hand solution of the power flow. Special purpose network analyzers
were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-

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scale digital computers replaced the analog methods with numerical solutions. In addition to a power-flow study,
computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient &
steady-state), unit commitment and economic dispatch.
[1]
In particular, some programs use linear programming to

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find the optimal power flow, the conditions which give the lowest cost per kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Get the input Value
Step 3: Calculate the Y bus impedance Matrix

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Step 4: Calculate P and Q by using formula,
P= Gen MW- Load MW;
Q= Gen MVA ? Load MVA;
Step 5: Check the condition for the loop
For i=2: bus and assume sum Y v =0

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Step 6: Check the condition of for loop
if for K=i:n bus and check if i=k and calculate
sum Y v= sum Y v + Y bus (i,k)*V(k)
Step 7: Check the condition for type if type(i)==2, Calculate Q(i)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 48

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Q(i)=-imag (conj(V(i))*(sum Yv+ Ybus (i,i)*V(i));
Step 8: Check the condition for Q(i) by using if loop
If Q(i)< Qmin(i)
Q(i)<=Q min(i)

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Else
Q(i)= Q max(i)
Step 9: Check the condition for type
V(i)=1/Ybus(i,i)*(P(i)-jQ(i)/Conj(V(i))-sum Yv);
Step 10: Iteration incremented

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Step 11: Find the angle value angle=180/Pi*angle(v)
Step 12: End the program
Procedure:
1 Enter the command window of the MATLAB
2 Create a new M ? file by selecting File - New ? M ? File.

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3 Type and save the program in the editor Window
4 Execute the program by pressing Tools ? Run
5 View the results
Exercise:
The figure shows the single line diagram of a simple 3 bus power system with generator at bus-1. The magnitude

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at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedances
are marked in p.u. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor
values of the voltage at the load bus 2 and 3. Find the slack bus real and reactive power and verify the results using
MATLAB.

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 49

Program:
clc
clear all

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sb=[1 1 2 4 3]; %input('Enter the starting bus = ')
eb=[2 3 4 3 2]; % input('Enter the ending bus = ')
nl=5; %input(' Enter the number of lines= ')
nb=4; %input(' Enter the number of buses= ')
sa=[1-5j 1.2-4j 1.1-2j 1.2-3j .5-4j]; %input('Enter the value of series impedance =')

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Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);
k2=eb(i) ;
y(i)=sa(i);

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Ybus(k1,k1)=Ybus(k1,k1)+y(i);%+h(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);%+h(i);
Ybus(k1,k2)=-y(i);
Ybus(k2,k1)=Ybus(k1,k2);
end

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Ybus
PG=[0 .5 .4 .2];
QG=[0 0 .3j .1j];
V=[1.06 1.04 1 1];
Qmin=.05;

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Qmax=.12;
for i=1:nb
Pg=PG(i);
Qg=QG(i);
if(Pg==0&&Qg==0)%for slackbus

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p=1;
Vt(p)=V(p) ;
end
if(Pg~=0&&Qg==0)%for Generator bus
for q=1:p-1

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A=Ybus(p,q)*V(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 50

end
B=0;

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for q=p:nb
B=B+Ybus(p,q)*V(q);
end
c=V(p)*(A+B);
Q=-imag(c)

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if(Qmin<=Q&&Q<=Qmax)%check for Q limt
Qg=Q*j;
Vt(p)=V(p);
else

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if(Q<=Qmin)
Q=Qmin;
else
Q=Qmax;
end

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Vt(p)=1;
disp('it is load bus')
Qg=Q*j
end
QG(p)=Qg;

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for q=1:p-1
A1=Ybus(p,q)*V(q);
end
B1=0;
for q=p+1:nb

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B1=B1-(((Ybus(p,q))*V(q)));
end
C1=((PG(p)-(QG(p)))/Vt(p));
Vt(p)=((C1-A1+B1)/Ybus(p,p));
elseif(Pg~=0&&Qg~=0)%for load bus

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A2=0;
for q=1:p-1
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 51

A2=A2-Ybus(p,q)*Vt(q);

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end
B2=0;
for q=p+1:nb
B2=B2-(((Ybus(p,q))*V(q)));
end

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C2=(-PG(p)+(QG(p))/V(p));
Vt(p)=((C2+A2+B2)/Ybus(p,p))
end
p=p+1;
end

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Output:
Y bus =
2.2000 - 9.0000i -1.0000 + 5.0000i -1.2000 + 4.0000i 0
-1.0000 + 5.0000i 2.6000 -11.0000i -0.5000 + 4.0000i -1.1000 + 2.0000i
-1.2000 + 4.0000i -0.5000 + 4.0000i 2.9000 -11.0000i -1.2000 + 3.0000i

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0 -1.1000 + 2.0000i -1.2000 + 3.0000i 2.3000 - 5.0000i


Q =
0.1456, it is load bus

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Q g =
0 + 0.1200i
V t =
1.0600 1.0476 + 0.0397i 1.0061 - 0.0148i 0.9899 - 0.0165i
Result:

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Thus, the mathematical formulation of power flow model in complex form and a simple method of solving power
flow problems of small sized system using Gauss-Seidel iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Gauss-Seidal algorithm is coded using MATLAB.

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Application:
Load flow studies are commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 52

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1. What is meant by load flow analysis?
Load flow studies determine if system voltages remain within specified limits under normal or emergency operating conditions,
and whether equipment such as transformers and conductors are overloaded
2. What is meant by acceleration factor?

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Gauss- Siedel method has simple calculations and is easy to execute. However, the convergence depends on the
acceleration factor
3. Define ? Slack Bus
The real power and voltage are specified for buses that are generators. These buses have a constant power generation,
controlled through a prime mover, and a constant bus voltage

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4. Define ? Generator Bus
The real power and voltage are specified for buses that are generators
5. What are the different types of buses in power system network?
Slack Bus, Generator Bus and Load Bus
6. What is meant by acceleration factor in load flow solution? What is its best value?

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acceleration factor value 1.6
7. List the advantages of Gauss-Siedal method.
Simplicity in technique
Small computer memory requirement
Less computational time per iteration

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8. List the advantages of load flow analysis.
Load flow studies are commonly used to Identify real and reactive power flow. Minimize kW and kVar losses
9. What is meant by P-Q bus in power flow analysis?
Load bus is P-Q bus
10. Define ? Primitive matrix

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z is a square matrix of size e ? e. The matrix z is known as primitive impedance matrix.
Viva - voce
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 53

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Expt.no.11: SOLUTION OF POWER FLOW USING NEWTON-
RAPHSON METHOD
Aim:
To determine the power flow analysis using Newton ? Raphson method
Software required:

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MATLAB 7.6
Theory:
The Newton Raphson method of load flow analysis is an iterative method which approximates the set of non-linear
simultaneous equations to a set of linear simultaneous equations using Taylor?s series expansion and the terms are
limited to first order approximation. Power-flow or load-flow studies are important for planning future expansion of

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power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive
power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the
power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-
scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical

--- Content provided by FirstRanker.com ---

solutions. In addition to a power-flow study, computer programs perform related calculations such as short-circuit
fault analysis, stability studies (transient & steady-state), unit commitment and economic dispatch.
[1]
In particular,
some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per

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kilowatt hour deliver.
Algorithm:
Step 1: Start the Program
Step 2: Declare the Variable gbus=6, ybus=6
Step 3: Read the Variable for bus, type , V, de, Pg, Qg, Pl, Ql, Q min, Q max

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Step 4: To calculate P and Q
Step 5: Set for loop for i=1:nbus, for k=1:nbus then calculate
P(i) & Q(i) End the Loop
Step 6: To check the Q limit Violation
Set if iter<=7 && iter>2

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Set for n=2: nbus
Calculate Q(G), V(n) for Qmin or Q max
End the Loop
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 54

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Step 7: Change from specified Value
Declare dPa= Psp-P
dQa= Qsp- Q
dQ= Zeros(npq,1)
Set if type(i)==3

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End the Loop
Step 8: Find Derivative of Real power injections with angles for Jacobian J1
Step 9: Find Derivative of Reactive power injections with angles for J3
Step 10: Find Derivative of Reactive power injections with voltage for J4 & Real power injections with
angles for J2

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Step 11: Form Jacobian Matrix J= [J1 J2;J3 J4]
Step 12: Find line current flow & line Losses
Step 13: Display the output
Step 14: End the Program
Exercise:

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 55

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1. Consider the 3 bus system each of the 3 line bus a series impedance of 0.02 + j0.08 p.u and a total
shunt admittance of j0.02 p.u. The specified quantities at the bus are given below.
Bus
Real load
demand, P D

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Reactive Load
demand, Q D
Real power
Generation, P G
Reactive Power

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Generation, Q G
Voltage
Specified
1 2 1 - - V 1=1.04
2 0 0 0.5 1 Unspecified

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3 1.5 0.6 0 Q G3 = ? ? V 3 = 1.04

2. Verify the result using MATLAB
Program:
%NEWTON RAPHSON METHOD

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clc
clear all
sb=[1 1 2]; %input('Enter the starting bus = ')
eb=[2 3 3]; % input('Enter the ending bus = ')
nl=3; %input(' Enter the number of lines= ')

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nb=3; %input(' Enter the number of buses= ')
sa=[1.25-3.75j 5-15j 1.667-5j]; %input('Enter the value of series impedance =')
Ybus=zeros(nb,nb);
for i=1:nl
k1=sb(i);

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k2=eb(i);
y(i)=(sa(i));
Ybus(k1,k1)=Ybus(k1,k1)+y(i);
Ybus(k2,k2)=Ybus(k2,k2)+y(i);
Ybus(k1,k2)=-y(i);

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Ybus(k2,k1)=Ybus(k1,k2);
end
Ybus
Ybusmag=abs(Ybus);
Ybusang=angle(Ybus)*(180/pi);

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% Calculation of P and Q
v=[1.06 1 1];
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P=[0 0 0];

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Q=[0 0 0];
del=[0 0 0];
Pg=[0 0.2 0];
Pd=[0 0 0.6];
Qg=[0 0 0];

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Qd=[0 0 0.25];
for p=2:nb
for q=1:nb
P(p)=P(p)+(v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q)));
Q(p)=(Q(p)+(v(p)*v(q)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q))));

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Pspe(p)=Pg(p)-Pd(p);
Qspe(p)=Qg(p)-Qd(p);
delP(p)=Pspe(p)-P(p);
delQ(p)=Qspe(p)-Q(p);
end

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end
P;
Q;
Pspe;
Qspe;

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delP;
delQ;

%Calculation of J1
P2=[0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
P1=2*v(p)*Ybusmag(p,q)*cos(angle(Ybus(p,q)));
for j=1:nb

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if (j~=p)
P2(q)=P2(q)+v(j)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(q,j))-del(j));
PV(p,q)=P1+P2(q);
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 57

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end
end
else
PV(p,q)=v(p)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end

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end
end
PV;
% Calculation of J2
Pdel=[0 0 0;0 0 0;0 0 0];

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for p=2:nb
for q=2:nb
if(p==q)
for j=1:nb
if(j~=p)

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Pdel(p,q)=Pdel(p,q)-v(j)*v(q)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(p,j))-del(j));
end
end
else
Pdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*sin(del(p)+angle(Ybus(p,q))-del(q));

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end
end
end
Pdel;
%Calculation of J3

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Q2=[0 0 0];
for p=2:nb
for q=2:nb
if(p==q)
Q1=2*v(p)*Ybusmag(p,q)*sin(-angle(Ybus(p,q)));

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for j=1:nb
if (j~=p)
Q2(q)=Q2(q)+v(j)*Ybusmag(q,j)*sin(del(q)-angle(Ybus(q,j))-del(j));
QV(p,q)=Q1+Q2(q);
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end
end
else
QV(p,q)=v(p)*Ybusmag(p,q)*sin(del(p)-angle(Ybus(p,q))-del(q));

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end
end

end
QV;

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%Calculation of J4
Qdel=[0 0 0;0 0 0;0 0 0];
for p=2:nb
for q=2:nb
if(p==q)

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for j=1:nb
if(j~=p)
Qdel(p,q)=Qdel(p,q)+v(j)*v(q)*Ybusmag(q,j)*cos(del(q)+angle(Ybus(p,j))-del(j));
end
end

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else
Qdel(p,q)=-v(p)*v(q)*Ybusmag(p,q)*cos(del(p)+angle(Ybus(p,q))-del(q));
end
end
end

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Qdel;
%Jacobian matrix
PV(1,:)=[ ];
PV(:,1)=[ ];
Pdel(1,:)=[ ];

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Pdel(:,1)=[ ];
QV(1,:)=[ ];
QV(:,1)=[ ];
Qdel(1,:)=[ ];
Qdel(:,1)=[ ];

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Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 59

J=[PV Pdel;QV Qdel]
%Find the change in v&del
delP(1:1)=[];

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delQ(1:1)=[];
delpq=[delP';delQ']
vdel=inv(J)*delpq
%Find new v&del
for i=1:nb-1

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for j=2:nb
vnew(i)=v(j)+vdel(i);
delnew(i)=del(j)+vdel(i+2);
end
end

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VNEW=[v(1) vnew]
DELNEW=[del(1) delnew
Output:
Ybus =
6.2500 -18.7500i -1.2500 + 3.7500i -5.0000 +15.0000i

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-1.2500 + 3.7500i 2.9170 - 8.7500i -1.6670 + 5.0000i
-5.0000 +15.0000i -1.6670 + 5.0000i 6.6670 -20.0000i
J =
2.8420 -1.6670 8.9750 -5.0000
-1.6670 6.3670 -5.0000 20.9000

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8.5250 -5.0000 -2.9920 1.6670
-5.0000 19.1000 1.6670 -6.9670
delpq =
0.2750
-0.3000

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0.2250
0.6500
vdel =
0.0575
0.0410

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0.0088
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Viva - voce
-0.0201

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VNEW =
1.0600 1.0575 1.0410
DELNEW =
0 0.0088 -0.0201
Result:

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Thus, the mathematical formulation of power flow model in complex form and for solving power flow problems of
small sized system using Newton Raphson iterative algorithm were obtained using MATLAB.
Outcome:
By doing the experiment, the power flow formulation using Newton- Raphson algorithm is coded using MATLAB.
Application:

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The Newton-Raphson method was applied to solve the thermal EHD lubrication model of line contacts. By
accounting for thermal effects in the Newton-Raphson scheme, a very stable numerical approach was obtained. Two
models with viscosity constant and variable across the oil film were developed.

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1. What is meant by jacobian matrix?
Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square
matrix, both the matrix
2. What are the different types of buses in power system network?
Slack bus, generator bus and load bus

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3. What are the information obtained from a load flow study?
The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each
bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for
hand solution of the power flow.
4. What is the need for load flow study?

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Load flow studies determine if system voltages remain within specified limits under normal or emergency operating
conditions, and whether equipment such as transformers and conductors are overloaded. Load flow studies are
commonly used to: Optimize component or circuit loading. Develop practical bus voltage profiles
5. What are the quantities associated with each bus in a system?
P.Q,V,?

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6. Define - Voltage Controlled Bus
Volatage Controlled buses where generators are connected. Therefore the power generation in such buses is controlled
through a prime mover while the terminal voltage is controlled through the generator excitation
7. What is the need for slack bus?
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The slack bus is the only bus for which the system reference phase angle is defined. From this, the various angular
differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with
maximum real power.

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8. What is meant by flat voltage start?
The value of flat voltage start 1+j0
9. What are the advantages of Newton Raphson method?
Newton Raphson method needs less number of iterations to reach convergence, takes less

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computation time
More accurate and not sensitive to the factors such like slack bus selection, regulation transformers
etc. and the number of iterations required in this method is almost independent of system size.
10. What are the disadvantages of Newton Raphson method?
More calculations involved in each iteration and require large computation time per iteration and

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large computer memory
Difficult solution technique (programming is difficult)


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Expt.No.12: FAULT ANALYSIS IN POWER SYSTEM
Aim:
To become familiar with modeling and analysis of power systems under faulted condition and to compute the fault
level, post-fault voltages and currents for different types of faults, both symmetric and unsymmetrical. To calculate

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the fault current, post fault voltage and fault current through the branches for a three phase to ground fault in a small
power system and also study the effect of neighboring system. Check the results using available software. To obtain
the fault current, fault MVA, Post-fault bus voltages and fault current distribution for single line to ground fault, line-to-
line fault and double line to ground fault for a small power system, using the available software.To Carryout fault
analysis for a sample power system for LLLG, LG, LL and LLG faults and prepare the report

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Software required:
MATLAB 7.6
Theory:
Short circuit studies are performed to determine bus voltages and currents flowing in different parts the system
when it is subjected to a fault. The current flowing immediately after the fault consists of an AC component which

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eventually reaches steady state and a fast decaying DC component which decays to zero. Only the AC component is
considered in the analysis. The analysis is done using phasor technique assuming the system to be under quasi-
steady state and is done for various types of faults such as three-phase-to ground, line-to-ground, line-to-line and
double-line-to-ground. The results of fault studies are used to select the circuit breakers, set protective relays and to
assess the voltage dips during fault. It is one of the primary studies to be performed whenever system expansion is

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planned.
Modeling details:
Approximations:
The following approximations are usually made in fault analysis:
1. Pre-fault load currents are neglected

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2. Transformer taps are assumed to be nominal
3. A symmetric three phase power system is considered
4. Transmission line shunt capacitance and transformer magnetizing impedances are ignored
5. Series resistances of transmission lines are neglected
6. The negative sequence impedance of alternators is assumed to be the same as their positive sequence

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impedance
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In the case of symmetrical faults, it is sufficient to determine the currents and voltages in one phase. Hence the
analysis is carried out on per phase basis (using + ve sequence Impedance network). In the case of unsymmetrical

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faults, the method of symmetrical components is used.
Sequence impedances of power system components:
The sequence impedances of power system components namely generators, transmission lines and transformers
are required for modeling and analysis of unsymmetrical faults. In the case of overhead transmission lines the
positive-and negative-sequence impedances are the same and the zero sequence impedance depends on ground

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wire, tower footing resistance and grounding adopted.
In the case of transformers, the positive-and negative- sequence impedances are the same and the zero
sequence impedance depends on transformer winding connection, method of neutral grounding and transformer type
(shell or core).The positive-, negative-and zero-sequence impedances are different in the case of rotating equipment
like synchronous generator, synchronous motor and induction motors. Estimation of sequence impedances of the

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components and assembling of zero-, positive-and negative-sequence impedance networks are the major steps in
unsymmetrical fault analysis.
Short circuit computation:
Symmetrical fault analysis:
Since the fault is symmetric the analysis is carried out on per phase basis. A short circuit represents a structural

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change in the network which is equivalent to the addition of impedance (in the case of a symmetric short, three equal
impedances) at the location of fault. The changes in voltages and currents that result from this structural change can
be analyzed using Thevenin?s theorem which states: The changes that occur in the network voltages and currents
due to the addition of an impedance between two network nodes are identical with those voltages and currents that
would be caused by an emf placed in series with the impedance and having a magnitude and polarity equal to the

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pre-fault voltage that existed between the nodes in question and all other sources being zeroed. The post-fault
voltages and currents in the network are obtained by superposing these changes on the pre-fault voltages and
currents.
Example1:
For the two-bus system shown in Fig .1, determine the fault current at the fault point and in other elements for a

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fault at bus 2 with a fault impedance Z f . Load current can be assumed to be negligible. The pre-fault voltages at all
the buses can be assumed to be 1.0 p.u. The sub transient reactance of the generators and positive sequence
reactance of other elements are given. Assume that the resistances of all the elements are negligible.
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Fig 1 Symmetrical fault on a two bus system

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First the ?Thevenin?s equivalent network? is formed Fig. 2a). The pre-fault voltage at bus2, V o2 equals 1.0 p.u. In
Fig 2a) the ?Thevenin?s emf? E th= V o2 = 1.0 is inserted in series with the short-circuit branch. The reduced Thevenin?s
equivalent circuit is given in Fig 2c). In which the ?Thevenin?s equivalent impedance ?Z th is found to be j0.144p.u. It
should be noted that Z th is nothing but the driving point impedance at bus 2 which is the same as the diagonal
element Z 22 of bus impedance matrix of the network. With reference to Fig 2c). The fault current is given by

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Fig. 2a)
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Fig. 2b)

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Fig. 2c) Development of thevenin?s equivalent circuit (all impedances are in per unit)

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This current is the total fault current fed by both the generators. The contribution from each generator can be
computed by noting that the total current divides in inverse impedance ratio.
Interconnections with neighboring systems:

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If a power system A, is interconnected to a neighboring system B, through, say a tie-line T 12, then for a fault at any
of the buses in system A all the generators in system B also will feed the fault through the tie-line. Instead of
representing the complete network of the system B, the Thevenin?s equivalent circuit of system B can be connected
at the tie bus 2, (Fig 5.3).
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The Thevenin?s equivalent reactance at bus 2 is given by
X Th, B = 1/SCC 2
Where SCC 2 is the fault level of Bus2.
Thevenin?s source E Th, B may be assumed as 1.0 p.u

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Fig. 3 Thevenin?s equivalent for neighboring system
Systematic computation for large scale systems:
The systematic computation procedure to be used for fault analysis of a large power systems using computer is
explained below. Let us consider a symmetric fault at bus r of an n-bus system. Let us assume that the pre-fault

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currents are negligible.
Step: 1
Draw the pre-fault per phase network of the system (positive sequence network) (Fig 5.4).Obtain the positive
sequence bus impedance matrix Z using Building Algorithm. All the machine reactance should be included in the Z
bus.

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Fig 4 Pre-fault per phase network (with loads neglected)
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Viva - voce
Step: 2
Obtain the falut current using the Thevenin?s equivalent of the system feeding the foult as explained below.
Assume fault impedance as Z

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f
. TH=he thevenin?s eqivalent of the system feeding the faulf impedance is given in
figure 5.5.

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Step: 3
Fig.5 Thevenin?s Equivalent of the system feeding the fault
Obtain the Thevenin?s Equivalent network
Result:

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Thus, the modeling and analysis of power systems under faulted condition and to compute the fault level, post-fault
voltages and currents for different types of faults were obtained using MATLAB.
Outcome:
By doing the experiment, the fault analysis in power system has been done using MATLAB and different types of
faults have been solved using MATLAB.

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Application:
Short Circuit Analysis is performed to determine the currents that flow in a power system under fault
conditions.A Short Circuit Analysis will help to ensure that personnel and equipment are protected by
establishing proper interrupting ratings of protective devices

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1. What is meant by fault?
In an electric power system, a fault or fault current is any abnormal electric current. For example, a short circuit is a fault in
which current bypasses the normal load.
2. What are the different types of fault?

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LG, LL ,LLG and symmetrical fault

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3. What are the assumptions made in fault analysis?
Transformers are on nominal tap position. This will let us take nominal voltages of transformers in
calculations.
All sources are balanced and equal in magnitude and phase. We neglect the slight differences in
magnitude and phase of the source voltages as it is nothing when compared with the fault.

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4. What is meant by bolted fault?
Bolted fault. Notionally, all the conductors are considered connected to ground as if by a metallic conductor; this is called a
"bolted fault
5. What are the different sequence networks in power system?
Positive sequence, negative sequence and zero sequence

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6. Why does fault occur in a power system?
An open-circuit fault occurs if a circuit is interrupted by some failure. ... In a "ground fault" or "earth fault", current flows into
the earth
7. How are the faults classified?
Symmetrical and unsymmetrical fault

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8. List out the various types of shunt and series faults.

Open conductor fault and symmetrical fault
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 69

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Expt.No.13: MODELING OF FACTS DEVICES USING
SIMULINK

Aim:
To simulate Facts device in order to control the reactive power flow in a line for efficient operation of the power

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system and transmission network
Software required:
MATLAB /SIMULINK
Theory:
Today?s power grids are driven closer to their transfer capacities due to the increased consumption and power

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transfers, endangering the security of the system. Flexible AC transmission systems (FACTS) have gained a great
interest during the last few years, due to recent advances in power electronics. On the other hand, FACTS devices
are a powerful technology that can solve many outstanding problems in power systems. FACTS devices have been
mainly used for solving various power system steady state control problems such as voltage regulation, power flow
control, and transfer capability enhancement. e.g. by improving the voltage profile or increasing the transfer capacity

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of a system without the need of new lines Generally, it is not cost-effective to install FACTS devices for the sole
purpose of power system stability enhancement.
Overview:
There are two generations for realization of power electronics-based FACTS controllers: the first generation
employs conventional thyristor-switched capacitors and reactors, and quadrature tap-changing transformers, the

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second generation employs gate turn-off (GTO) thyristor-switched converters as voltage source converters (VSC?s).
The thyristor-controlled group employs capacitor and reactor banks with fast solid-state switches in traditional shunt
or series circuit arrangements. The thyristor switches control the on and off periods of the fixed capacitor and reactor
banks and thereby realize a variable reactive impedance. Except for losses, they cannot exchange real power with
the system. The voltage source converter (VSC) type FACTS controller group employs self-commutated DC to AC

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converters, using GTO thyristors, which can internally generate capacitive and inductive reactive power for
transmission line compensation, without the use of capacitor or reactor banks. The converter with energy storage
device can also exchange real power with the system, in addition to the independently controllable reactive power.
The VSC can be used uniformly to control transmission line voltage, impedance, and angle by providing reactive
shunt compensation, series compensation, and phase shifting, or to control directly the real and reactive power flow

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in the line.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 70


Series compensation:

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In series compensation, the FACTS is connected in series with the power system. It works as a controllable
voltage source. Series inductance occurs in long transmission lines, and when a large current flow causes a large
voltage drop. To compensate, series capacitors are connected.

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Shunt compensation:
Fig 1. Series Compensation

In shunt compensation, power system is connected in shunt (parallel) with the FACTS. It works as a controllable
current source.

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Fig 2. Shunt Compensation
First generation of Facts devices:
1. Static VAR Compensator (SVC)

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2. Thyristor-Controlled Series Capacitor (TCSC)
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 71

3. Thyristor-Controlled Phase Shifter (TCPS)
Second generation of Facts devices:

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1. Static Compensator (STATCOM)
2. Static Synchronous Series Compensator (SSSC)
3. Unified Power Flow Controller (UPFC)
Series compensation:
FACTS for series compensation modify line impedance: X is decreased so as to increase the transmittable active

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power. However, more reactive power must be provided.

Shunt compensation:
Reactive current is injected into the line to maintain voltage magnitude. Transmittable active power is increased but
more reactive power is to be provided.

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Simulink block diagram:
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 72

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Output:


Result:

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Thus, simulation of facts device in order to control the reactive power flow in a line for efficient operation of the
power system and transmission network were obtained using MATLAB/simulink.
Format No. FirstRanker/Stud/LM/34/Issue:00/Revision:00 73

Outcome:

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By doing the experiment, the modeling of Facts devices using MATLAB / SImulink has been done.
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