A Project Report Submitted in partial fulfillment of the requirements for the degree of

Bachelor of Technology in Electrical Engineering By

PRANAMITA BASU ( Roll No. – 10502064 ) AISWARYA HARICHANDAN ( Roll No. – 10502019 )

National Institute of Technology Rourkela Rourkela-769008, Orissa

POWER SYSTEM STABILITY STUDIES USING MATLAB

A Project Report Submitted in partial fulfillment of the requirements for the degree of

Technology Bachelor of Technology in Electrical Engineering By PRANAMITA BASU ( Roll No. – 10502064 ) AISWARYA HARICHANDAN ( Roll No. – 10502019 )

Under the guidance of PROF. P.C. PANDA

National Institute of Technology Rourkela Rourkela-769008, Orissa 2

NATIONAL INSTITUTE OF TECHNOLOGY, ROURKELA

CERTIFICATE

This is to certify that the project entitled “POWER SYSTEM STABILITY USING MATLAB” submitted by Ms. Pranamita Basu ( Roll No. 10502064 ) and Ms. Aiswarya Harichandan (Roll No. 10502019 in partial fulfillment of the requirements for the award of Bachelor of Technology Degree in Electrical Engineering at NIT Rourkela is an authentic work carried out by them under my supervision and guidance.

Date: Rourkela

(Prof. P. C. Panda) Dept. of Electrical Engg. National Institute of Technology Rourkela-769008, Orissa

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ACKNOWLEDGEMENT

I would like to thank NIT Rourkela for giving me the opportunity to use their resources and work in such a challenging environment. .

First and foremost I take this opportunity to express my deepest sense of gratitude to my guide Prof. P. C. Panda for his able guidance during my project work. This project would not have been possible without his help and the valuable time that he has given me amidst his busy schedule.

I would also like to extend my gratitude to my friends and senior students of this department who have always encouraged and supported me in doing my work.

Last but not the least I would like to thank all the staff members of Department of Electrical Engineering who have been very cooperative with us.

Pranamita Basu Aiswarya Harichandan

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CONTENTS

Certificate Acknowledgement Contents List of Figures Abstract 1. Introduction 2. Study of Swing Equation 2.1 Stability 2.2 Swing Equation 3. Steady State Stability 3.1 Analysis of Steady-State Stability by Swing Equation 3.2 Damping Torque 3.3 Illustration 3.4 Matlab Code 3.5 Waveforms for Steady-State Analysis 4. Transient Stability Studies 4.1 Numerical Solution of Swing Equation 4.2 Illustration 4.3 Matlb Code 4.4 Simulink Design 4.5 Output Waveforms 4.6 Point-by-Point Method 4.7 Matlab Code for Point-By-Point Method 4.8 Outputs 03 04 05 08 10 11 13 14 15 17 18 19 20 21 22 23 24 25 25 34 35 38 40 42

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5. Multimachine System Analysis 5.1 Mutimachine Systems 5.2 Illustration 5.3 Matlab Code 5.4 Output Waveforms 6. Small Signal Stability Including Effects of Rotor Circuit Dynamics 6.1 Small Signal Stability 6.2 Effect of Synchronous Machine Field Circuit Dynamics 6.2.1 Synchronous Machine Equations 6.2.2 Network Equations 6.2.3 Linearized System Equations 6.2.4 Representing Saturation in Small-Signal Studies 6.2.5 Summary of Procedure for Formulating the State Matrix 6.3 Block Diagram Representation 6.3.1 Expressions for K Constants in Expanded Form 6.3.2 Effect of Field Flux Linkage Variation on System Stability 6.3.3 Special Situations with K4 negative 6.4 Illustration 6.5 Matlab Code 6.6 Results 7. Transient Stability Analysis Including Damping 7.1 An Elementary View of Transient Stability 7.2 Response to a Step Change in Pm 7.3 Response to a Short Circuit Fault` 7.4 Factors Affecting Transient Stability 7.5 Numerical Integration Methods 7.5.1 Runge-Kutta (R-K) Methods 7.5.1.1 Second-order R-K Method 7.5.1.2 Fourth-order R-K Mehtod 7.6 Illustration 7.7 Solution

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7.8 Matlab Code 7.9 Results 7.10 Simulation of...