Power System Analysis

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Power System Analysis

Prof. P.S.R. Murthy

B.Sc. (Engg.) (Hons.) ME.,

Dr. - ING (Berlin), F.I.E. (India)

Life Member - ISTE

(Formerly Principal O.U. College of Engineering & Dean, Faculty of Engineering, O.U. Hyderabad)

Principal, Sree Datha Institute of Engineering and Science, Sheriguda, Ibrahim Patnam, Hyderabad (AP).

BSP BS Publications 4-4-309, Giriraj Lane, Sultan Bazar, Hyderabad - 500095 A.P. Phone: 040-23445688

Copyright 2007, by Publisher All rights reserved

No part of this book or parts thereof may be reproduced, stored in a retrieval system or transmitted in any language or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publishers.

Published by :

SSP BS Publications 4-4-309, Giriraj Lane, Sultan Bazar, Hyderabad - 500 095 A. P. Phone: 040-23445688 e-mail: contactus@bspublications.net www.bspublications.net

Printed at:

AdithyaArt Printers

Hyderabad.

ISBN: 978-81-7800-161-6

Preface

Power System analysis is a pre-requisite course for electrical power engineering students.

In Chapter I. introductory concepts about a Power system, network models, faults and analysis;the primitive network and stability are presented.

Chapter 2 deals with the graph theory that is relevant to various incidence matrices required for network modelling are explained.

Chapter 3 explains the various incidence matrices and network matrices.

Chapter 4 discusses, step-by-step method of building of network matrices.

Chapter 5 deals with power flow studies. Both Gauss-Seidel method and Newton-Raphson methods are explained. In Newton-Raphson method both the Cartesion coordinates method and polar coordinates methods are discussed.

In chapter 6 short circuit analysis is explained Per unit quantity and percentage values are defined. Analysis for symmetrical faults is discussed. The utility of reactors for bus bar and generator protection is also explained.

Unbalanced fault analysis is presented in chapter 7. Use of symmetrical components and network connections are explained.

Chapter 8 deals with the power system stability problem. Steady state stability. transient stability and dynamic stability are discussed.

It is earnestly hoped that this book will meet the requirements of students in the subject power system analysis.

- Author

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Acknowledgment

My sincere thanks go to Mr. Nikhil Shah, Proprietor of BS Publications for his constant

encouragement to me to write and complete this book on 'Power System Analysis'.

My thanks also go to Mr. M.Y.L. Narasimha Rao, my well wisher for taking great pains in

transferring script material and proof material between my residence and the press with a great

smiley face, day and night over the last few months.

I thank Mrs. Swarupa for MATLAB assistance.

-Author

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Contents

Preface .................................................................................................................. (vii)

Acknowledgment ................................................................................................... (ix)

1 Introduction I. I The Electrical Power System .................................................................. I

1.2 Network Models ...................................................................................... 3

1.3 Faults and Analysis .................................................................................. 3

1.4 The Primitive Network ............................................................................ 4

1.5 Power System Stability ........................................................................... 5

2 Graph Theory 2.1 Introduction ............................................................................................. 6

2.2 Definitions ................................................................................................ 6

2.3 Tree and Co-Tree .................................................................................... 8

2.5 Cut-Set .................................................................................................... 9

2.4 Basic Loops ............................................................................................. 9

2.6 Basic Cut-Sets ....................................................................................... 10

vVorked Examples .. ' .... .. II

Prohlems ....... IS

Questions 16

(xii) Content~

3 Incidence Matrices 3.1 Element Node Incidence Matrix ............................................................ 18

3.2 Bus Incidence Matrix ............................................................................ 18

3.3 Branch - Path Incidence Matrix K ....................................................... 19

3.4 Basic Cut-Set Incidence Matrix ............................................................ 20

3.5 Basic Loop Incidence Matrix ................................................................. 21

3.6 Network Performance Equations .......................................................... 22

3.7 Network Matrices .................................................................................. 24

3.8 Bus Admittance Matrix and Bus Impedance Matrix ............................. 25

3.9 Branch Admittance and Branch Impedance Matrices ........................... 26

3.10 Loop Impedance and Loop Admittance Matrices ................................. 28

3.11 Bus Admittance Matrix by Direct Inspection ........................................ 29

Worked Examples. ...... ... ..... ........ ....... ............ . ................................ 33

Problems ........................... : ..................................................... 51

Questions .......... ........................................... '" .......................... 52

4 Building of Network Matrices 4.1 Partial Network ...................................................................................... 53

4.2 Addition ofa Branch .............................................................................. 55

4.3 Addition ofa Link .................................................................................. 60

4.4 Removal or Change in Impedance of Elements with Mutual Impedance ................................................................................. 66

Worked Examples. ........ " .. . 70

Problems .. . .............. : ............ . .... 96

Questions. . ............. . . ............. 97

5 Power Flow Studies 5.1 Necessity for Power Flow Studies ....................................................... 98

5.2 Conditions for Successful Operation of a Power System .................... 99

5.3 The Power Flow Equations ................................................................... 99

5.4 Classification of Buses ........................................................................ 101

5.5 Bus Admittance Formation .................................................................. 102

5.6 System Model for Load Flow Studies ................................................ 104

5.7 Gauss-Seidel Iterative Method ............................................................ 105

5.8 Gauss - Seidel Iterative Method of Load Flow Solution .................... 106

5.9 Newton-Raphson Method ................................................................... 109

5.9.1 The Rectangular Coordinates Method .................................. 110

5.9.2 The Polar Coordinates Method ............................................ 112

Contents (xiii)

5.10 Sparsity of Network Admittance Matrices .......................................... 115

5.11 Triangular Decompostion .................................................................... 116

5.12 Optimal Ordering ................................................................................. 118

5.13 Decoupled Methods ............................................................................. 119

5.14 Fast Decoupled Methods ..................................................................... 120

5.15 Load Flow Solution Using Z Bus ..................................................... 121

5.15.1 Bus Impedance Formation ................................................... 121

5.15.2 Addition of a Line to the Reference Bus .............................. 122

5.15.3 Addition of a Radial Line and New Bus ............................... 122

5.15.4 Addition of a Loop Closing Two Existing Buses in the System ............................................................. 123

5.15.5 Gauss - Seidel Method Using Z-bus for Load Flow Solution .............................................................. 124

5.16 Convergence Characteristics ............................................................... 124

Worked Examples ..... .... . . 126

Problems .............. 161

Questions ................................. . . ... . ........................ 175

6 Short Circuit Analysis 6.1 Per Unit Quantities ............................................................................... 176