Energy Systems in Electrical Engineering

Series editor

Muhammad H. Rashid, Pensacola, USA

More information about this series at http://www.springer.com/series/13509

Kabir Chakraborty · Abhijit Chakrabarti

1 3

Soft Computing Techniques in Voltage Security Analysis

Kabir ChakrabortyElectrical Engineering Department Tripura Institute of Technology AgartalaTripuraIndia

ISSN 2199-8582 ISSN 2199-8590 (electronic)Energy Systems in Electrical EngineeringISBN 978-81-322-2306-1 ISBN 978-81-322-2307-8 (eBook)DOI 10.1007/978-81-322-2307-8

Library of Congress Control Number: 2015932428

Springer New Delhi Heidelberg New York Dordrecht London© Springer India 2015This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made.

Printed on acid-free paper

Springer (India) Pvt. Ltd. is part of Springer Science+Business Media (www.springer.com)

Abhijit ChakrabartiElectrical Engineering DepartmentIndian Institute of Engineering Science

and Technology, ShibpurHowrahWest BengalIndia

Dedicated to

My ParentsMr. Kalyan ChakrabortyandMrs. Anjali Bhattacharjee

—Dr. Kabir Chakraborty

vii

Preface

Voltage security is recognized as a key issue for power systems operation. The con-tinuous increase in loads, along with economic and environmental constraints, has led the systems to operate close to their limits, and this includes voltage security limits. Academicians as well as practicing engineers are switching over to stud-ies of the numerous problems associated with the planning and operation of large interconnected power systems. Courses in power system analysis are being updated to reflect the importance of new tools such as computer, control, and systems theory. During the last 30 years, several papers and conference reports on power system voltage security have been published throughout the world, indicating the continuing interest of electrical engineers in this field. During these years, this sub-branch of electrical engineering has also come in quite close contact with a number of related disciplines such as optimal control theory, digital techniques, etc.

To maintain power systems security, it is essential to keep the operation within a specified margin of real and reactive power flow and this is usually mandated by the local reliability organizations. These margins are calculated from offline studies, thus it takes a good amount of time to figure out such margin points. The human operators in the control centers then utilize these conservatively tabulated values for secure power system operation. In this book, different approaches to improve such operational procedures are highlighted.

Remarkable advances in research in the field of power system security analysis for the computation of power system security margins have been noticed in the last 30 years. In the meantime, the extraordinary development in computational rates of recent computers has brought online security study closer to realistic utili-zation. In recent days, to satisfy the increasing power demands of consumers, the power system operating conditions are changed in an irregular fashion. For that, it is necessary to recompute the system security margins precisely to confirm secure operation of the systems, which is computationally infeasible. Presently, the use of soft computing techniques in voltage security study has picked up because of its capacity to do parallel data handling with high precision and quick response times. “Soft computing”, rather than routine “hard computing”, is a procedure that is tolerant of indecision, imprecision, incomplete truth, and rough guesses.

Prefaceviii

The soft computing techniques are modeled on the concept of the human brain, for which these are termed as Artificial Intelligence. These methods are fit for arriving at substantial conclusions based on deficient and fractional information obtained from prior knowledge just like in the human brain. Soft computing pro-cesses use an approximation of this concept on a very small scale. It is economical and consumes less time. Different branches of soft computing techniques are now available; among them three major branches are genetic algorithms, artificial neu-ral networks, and fuzzy logic. In this book, Artificial Neural Network (ANN) has been chosen as a soft computing tool, since, such networks are eminently suitable for the study of voltage security. The different architectures of the ANNs used in this book are selected on the basis of the intelligent criteria rather than by a “brute force” method of trial and error with different architectures.

The fundamental aim of this book is to present a comprehensive treatise in order to study the power system security and simulation of power system security studies. The topics are substantiated by suitable illustrations and computer methods and describe analytical aspects of operation and characteristics of power system from the viewpoint of voltage security.

The number of books dealing only with the problem of power system security is, rather low, especially in consideration of the rapid growth of this topic in recent years. Most of the advanced books devote only a chapter to the topic of power system security/stability. However, the versatile concepts used in different aspects of security need a much more thorough discussion. This fact stimulated us to make an effort to prepare a book that would cover fairly the concepts and problems of power system security. Besides that, in this book a number of MATLAB programs related to voltage stability/security are provided and some basic chapters like load flow analysis are also included.

The text is self-contained and thorough. It is intended for senior undergraduate students and postgraduate students in Electrical Engineering. Practicing engineers, Electrical Control Center (ECC) operators and researchers will also find the book suitable for their use.

Any constructive criticism and suggestion in improving the book further will be highly appreciated.

January 2015 Kabir ChakrabortyAbhijit Chakrabarti

ix

Acknowledgments

The authors are pleased to acknowledge the assistance given by a number of people including their students. Special acknowledgment is due to Dr. Abhinandan De, a faculty in Department of Electrical Engineering, Indian Institute of Engineering, Science and Technology, Shibpur, for his technical support. The authors acknowledge the help rendered by Dr. Dipanjana Chakraborty in checking the proof of the entire text. Kabir Chakraborty appreciates the patience and sup-port of his parents and child (Karnak) during the long period devoted in preparing the book. The support and encouragement of Swati Meherishi, Publishing Editor and Aparajita Singh, Editorial Assistant of Springer is also acknowledged.

January 2015 Kabir ChakrabortyAbhijit Chakrabarti

xi

Contents

1 Voltage Security—An Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Basic Components of Power System . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Threats to Power System Security . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Reasons for Power System Blackout . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Necessity for Voltage Security Analysis . . . . . . . . . . . . . . . . . . . . . . . 61.6 Application of Soft Computing Techniques

in Voltage Security Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Load Flow Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Formation of Admittance Matrix [YBus] . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1 [YBus] of a π-Equivalent Model of a 2-Bus System . . . . . . . . 142.2.2 Formation of [ZBus] from [YBus] . . . . . . . . . . . . . . . . . . . . . . . 152.2.3 MATLAB Programs for Formation of YBus . . . . . . . . . . . . . . 172.2.4 Modification of YBus Due to Presence

of Transformer in the Line . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2.5 MATLAB Program for Formation of Modified YBus . . . . . . . 24

2.3 Power Flow Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.3.1 Classification of Bus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.3.2 Power Flow Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.4 Gauss-Seidel (G–S) Method of Power Flow . . . . . . . . . . . . . . . . . . . 332.5 Newton–Raphson Method of Power Flow . . . . . . . . . . . . . . . . . . . . . 352.6 Fast Decoupled Method of Power Flow . . . . . . . . . . . . . . . . . . . . . . . 482.7 Line Power Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Contentsxii

3 Voltage Stability and Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 593.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.2 Voltage Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.3 Voltage Collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.3.1 Factors Affecting Voltage Collapse . . . . . . . . . . . . . . . . . . . . 623.3.2 Mechanism of Voltage Collapse . . . . . . . . . . . . . . . . . . . . . . . 63

3.4 Voltage Stability for a Two-Bus System . . . . . . . . . . . . . . . . . . . . . . . 643.4.1 Determination of Critical System Reactance

at Voltage Stability Limit at Any Power Factor . . . . . . . . . . . 663.4.2 Determination of Critical Receiving-End Voltage

and Critical Power Angle at Voltage Stability Limit for Two-Bus Power System . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.5 Contingency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.6 Voltage Security Analysis (VSA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4 Voltage Security Analysis by Classical Methods . . . . . . . . . . . . . . . . . . 754.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.2 Determination of Weakest Bus Using

“Reactive Power Sensitivity” as an Indicator . . . . . . . . . . . . . . . . . . . 764.2.1 An Offline Simulation Method to Identify

the Weakest Bus of a Multi-bus Power Network . . . . . . . . . . 764.3 Determination of Voltage Collapse Point Using

Conventional P–V and Q–V Curves . . . . . . . . . . . . . . . . . . . . . . . . . . 794.3.1 Offline Simulation Method of Voltage Security Analysis

of a 25-Bus Power Network Using P–V and Q–V Curves . . . 794.3.2 Effect of Tap-Changing Transformer on P–V Curve . . . . . . . 82

4.4 Determination of Voltage Collapse Point Using Singularity Criterion of Jacobian Matrix . . . . . . . . . . . . . . . . . . . . . . 834.4.1 Offline Simulation Method of Voltage Security

Analysis of a 25-Bus Power Network Using Singularity Criterion of Jacobian Matrix . . . . . . . . . . . . . . . . 84

4.4.2 Contingency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.5 Investigation of Voltage Stability Using P–Q Boundary . . . . . . . . . . 87

4.5.1 MATLAB Program for Determination of P–Q Boundary . . . 894.5.2 MATLAB Program for Plotting Theoretical P–V

for a Fixed Load Power Factor . . . . . . . . . . . . . . . . . . . . . . . . 904.5.3 Voltage Security Analysis of 25-Bus Power Network

Using P–Q and P–V Characteristics . . . . . . . . . . . . . . . . . . . . 904.5.4 Voltage Security Analysis of a Standard 30-Bus

Power Network Using P–Q Boundary . . . . . . . . . . . . . . . . . . 934.6 Reactive Power Compensation Method . . . . . . . . . . . . . . . . . . . . . . . 98

4.6.1 Modeling of the SVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.6.2 Effect of SVC Installation and Contingency Analysis . . . . . . 100

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4.7 Voltage Security Assessment Using Linear Voltage Stability Indicator (LVSI) Based on Reduced System Model . . . . . . . . . . . . . 1034.7.1 Concept of Equivalent 2-Bus Network . . . . . . . . . . . . . . . . . . 1034.7.2 Linear Voltage Stability Indicator (LVSI) . . . . . . . . . . . . . . . 1044.7.3 MATLAB Program for the Determination

of LVSI Index of a System . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.7.4 Voltage Security Assessment LVSI Based

on Reduced System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 1084.8 Integrated Voltage Stability Indicator (IVSI) Formulation . . . . . . . . . 109

4.8.1 Voltage Security Analysis of IEEE-57 Bus System Using IVSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

5 Soft Computing Techniques—An Overview . . . . . . . . . . . . . . . . . . . . . . 1195.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.2 Artificial Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

5.2.1 Fundamentals of Artificial Neural Networks . . . . . . . . . . . . . 1215.2.2 Properties of Artificial Neural Networks . . . . . . . . . . . . . . . . 1225.2.3 The Architecture of a Neuron . . . . . . . . . . . . . . . . . . . . . . . . . 122

5.3 Learning Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235.4 Application of ANNs in Voltage Security Analysis . . . . . . . . . . . . . . 124References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

6 Multilayer Perceptron (MLP) with Error Back-Propagation Learning in Voltage Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.2 The Single Perceptron Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 127

6.2.1 Perceptron Learning Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.3 Multilayer Perceptron (MLP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.3.2 The MLP Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.3.3 Error Back-Propagation Algorithm . . . . . . . . . . . . . . . . . . . . 1316.3.4 Methods for Improving Performance

in Back-Propagation Learning . . . . . . . . . . . . . . . . . . . . . . . . 1326.3.5 Improvement of Generalization . . . . . . . . . . . . . . . . . . . . . . . 132

6.4 Application of MLP and Back-Propagation in P–V and P–Q Characteristics Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 1336.4.1 Identification of Voltage Collapse Point Using MLP . . . . . . . 1336.4.2 Application of MLP and Simulation . . . . . . . . . . . . . . . . . . . 1346.4.3 Contingency Evaluation of Using ANN . . . . . . . . . . . . . . . . . 1416.4.4 ANN-Based MATLAB Program for Modeling

of P–Q and P–V Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1426.5 Assessment of Voltage Security Using ANN and LVSI . . . . . . . . . . . 143

6.5.1 Development of the ANN-Based Pattern Recognition Engine—Training and Exploitation . . . . . . . . . . . . . . . . . . . . 144

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6.6 Integrated Voltage Stability Index Approach for Assessment of Voltage Security . . . . . . . . . . . . . . . . . . . . . . . . . . 149

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

7 Classification of Voltage Security States Using Unsupervised ANNs . . . 1537.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1537.2 The Self-organizing Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

7.2.1 Brain Map and SOFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1557.2.2 The Kohonen’s Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1567.2.3 The Kohonen’s SOM Algorithm . . . . . . . . . . . . . . . . . . . . . . 158

7.3 Power System State Classification Using Kohonen’s SOFM . . . . . . . 1597.3.1 Case Study with IEEE-57 Bus System . . . . . . . . . . . . . . . . . . 1597.3.2 Case Study with Real-Time 203 Bus System . . . . . . . . . . . . . 164

7.4 MATLAB Program for Pattern Classification Using SOFM . . . . . . . 1697.5 Application of Intelligent Pattern Classification

Technique Based on SOFM in Real-Time System . . . . . . . . . . . . . . . 1707.5.1 Energy Control Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1707.5.2 Supervisory Control and Data Acquisition (SCADA) . . . . . . 1707.5.3 Framework of Central EMS Including

ANN-Based Pattern Classification Technique . . . . . . . . . . . . 171References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

8 Classification of Voltage Security States Using Supervised ANNs . . . . 1758.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1758.2 Learning Vector Quantization (LVQ) Algorithm

for Fine Tuning the Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1768.3 Testing and Fine Tuning of Classification Process with LVQ . . . . . . 1788.4 Radial Basis Function (RBF) Neural Network

for Pattern Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1808.4.1 Architecture of RBF Network . . . . . . . . . . . . . . . . . . . . . . . . 1808.4.2 Training of RBF Network . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

8.5 Improvement of Classification Process by RBF . . . . . . . . . . . . . . . . . 1828.6 Probabilistic Neural Network (PNN) . . . . . . . . . . . . . . . . . . . . . . . . . 184

8.6.1 Probabilistic Neural Network Architecture . . . . . . . . . . . . . . 1848.7 Classification by PNN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Appendix I: 25-Bus Sample Test System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Appendix II: IEEE 30-Bus Test System (American Electric Power) . . . . . 193

Appendix III: IEEE 57-Bus Test System (American Electric Power) . . . . 197

Contents xv

Appendix IV: 203-Bus Real System (A Power Utility of India) . . . . . . . . . 203

Suggested Readings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

xvii

About the Authors

Dr. Kabir Chakraborty was born in Dharmanagar, Tripura, India, on August 5, 1978. He is currently Assis-tant Professor of Electrical Engineering at Tripura Institute of Technology, Narsingarh, Tripura, India. He is a former Head of the department of Electrical Engineering of Tripura Institute of Technology. He holds B.Sc. (Physics Hons.) from Assam University in 2000 and B.Tech and M.Tech in Electrical Engineering from the University of Calcutta in 2003 and 2005 respectively. He completed his Ph.D. in 2013 from Indian Institute of Engineering Science and Technology (IIEST), Shibpur, (Formerly Bengal En-gineering and Science University, Shibpur) West Bengal,

India. He has more than 10 years of teaching and research experience. His areas of re-search interest include Voltage Stability and Artificial Neural Networks. He has published several papers in international and national journals and conference proceedings.

Prof. Abhijit Chakrabarti is currently Professor of Electrical Engineering at Indian Institute of Engineering Science and Technology (IIEST), Shibpur, (Formerly Bengal Engineering and Science University, Shibpur) West Bengal, India. He is a Former Vice-Chancellor of Jadavpur University and former Vice Chairman of West Bengal State Council of Higher Education. His areas of research interest are Electrical Power System Engineer-ing (Specially Voltage Stability, Economic Operation, Deregulation, and Congestion Management and FACTS

Devices). He completed his Ph.D. in 1991 from Calcutta University. He holds B.Tech from NIT, (Formerly R.E. College), Durgapur and M.Tech from IIT Delhi in 1978 and 1987 respectively. He has 7 years of industrial and 27 years of teaching and research experience. He also has to his credit 13 books and 121 contributed papers in journals and conferences. Dr. Chakrabarti is a Fellow of The Institution of Engineers (India).