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Assessment of Power System Reliability ˇ epin Marko C Assessment of Power System Reliability Methods and Applications 123 Prof. Dr. Marko C ˇ epin Faculty of Electrical Engineering University of Ljubljana Trzaska 25 1000 Ljubljana Slovenia e-mail: [email protected] ISBN 978-0-85729-687-0 e-I...

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Assessment of Power System Reliability

ˇ epin Marko C

Assessment of Power System Reliability Methods and Applications

123

ˇ epin Prof. Dr. Marko C Faculty of Electrical Engineering University of Ljubljana Trzaska 25 1000 Ljubljana Slovenia e-mail: [email protected]

ISBN 978-0-85729-687-0 DOI 10.1007/978-0-85729-688-7

e-ISBN 978-0-85729-688-7

Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Ó Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

To Alenka, Katarina and Irena

Preface

The importance of power system reliability, which is the subject of this book, is demonstrated, when people are confronted with the loss of electrical energy. This is true, no matter if the loss causes stopping of the production lines or even the shutdown of our companies, which can consequently cause huge economic deficits, or the loss of electrical energy only slightly decreases the comfort of our free time in our homes. Fortunately, such events happen rarely, because the reliability of modern power systems is high. Our aim for the reliability is connected to its constant improvement as this is in relation to the progress of the modern world. The objective of this book is to contribute to such improvement. The book is divided to six parts, which comprise 20 chapters. Part I of this book is related to introductory chapters comprising the background issues important to power system reliability. Chapter 1 briefly touches the history of power systems, which evolved from early days of discovering the electrical energy to today, and which is expected to be expanded in the future with new technologies, new features and new application fields. Chapter 2 presents short writing about selected blackouts, which are some of the main issues with which the power system reliability has to face. As the complexity of the systems increases in general, it is expected that the undesired events such as blackouts may result in larger consequences. Chapter 3 gives the main definitions of reliability and connected parameters. The largest difficulty of these definitions is that their use and understanding through different technical disciplines is not always the same. Chapter 4 summarizes the probability theory, which represents the background for reliability calculations. The probability theory and its implications can be very complex, but only their features, which facilitate the reliability evaluations of power systems, are emphasized inside this book. Part II of this book is related to reliability methods, which can be used for analyses of technical systems and processes. Chapter 5 presents the fault tree analysis, and the procedure for its practical applications is given. The identification and evaluation of important factors are presented. Chapter 6 shortly describes the event tree analysis, which is a method for evaluation of scenarios. Chapter 7 vii

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presents the binary decision diagram, which is a directed graph that consists of nodes and edges and that deals with Boolean logic. Chapter 8 gives the Markov processes, where the states of the components and the systems and the transitions between them are evaluated. Chapter 9 describes the reliability block diagram, which is the least abstract of the reliability methods. Chapter 10 deals with common cause failures, which represent the evaluation of dependent events and are important for consideration in redundant systems. Part III of this book is related to the methods of the power flow analysis, because the dynamic aspect of the power system is an important part of the related reliability assessments. Chapter 11 includes brief overview of the selected power flow methods. Part IV is the most important part of this book. It is related to various aspects of assessing the reliability of the power system and its parts. Chapter 12 presents the generating capacity methods including practical examples. Chapter 13 lists the reliability and performance parameters of selected power plants, which gives information about their successful operation from various points of view. Chapter 14 is oriented to distribution system reliability measures. This chapter may be understood as the most important chapter of this part, because the larger number of difficulties with power system reliability is connected with distribution systems. Chapter 15 gives a power system reliability method, which in addition to its static feature of assessing the static power system configuration includes the dynamics of the system in a certain way. The extent of power flows through the portions of the system that may impact the calculation of the power system reliability. Part V of this book is related to the optimization methods. The field of optimization methods is very wide and many methods exist. Only the selected methods among those that may be the most applicable for the tasks connected with reliability improvement are mentioned. Chapter 16 shortly presents the linear programming, which is among the simplest methods aimed to solve problems in terms of linear equalities and inequalities. Chapter 17 gives the dynamic programming and its main feature is that it transforms a complex problem into a sequence of simpler problems. Chapter 18 summarizes the genetic algorithms, which is a step toward solving nonlinear problems. Chapter 19 describes briefly the simulated annealing, which is another method for solving nonlinear problems, where the local minima should be avoided when finding the global one. Part VI of this book is related to the application of reliability and optimization methods. Chapter 20 represents a wide field with many reliability applications and optimizations, from which only some selected ones are presented. The index at the end includes the most important terms related to the subjects of the book and identifies their placement in the book. The chapters of the book have been aimed to be written in a simple language without very detailed theoretical and mathematical abstraction of specific methods and their applications. Rather, the practical use of the materials directed the writing of the book. This book contains simple examples in most of the chapters or within their sections in order to facilitate the understanding of the theory behind.

Preface

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Each chapter includes a list of references, which support the content of the chapter. The Internet addresses of some references, which are available at the time of writing the book, are provided. In addition, several references may exist on the Internet, which were not available at the time of writing of the book, or the Internet address of existing information may change, so the readers of this book are encouraged to search the Internet for the supporting references of their interest. It is suggested that the search is made by putting the title of the reference in brackets in order to reduce the list of unnecessary results, e.g. search of ‘‘component reliability data for use in probabilistic safety assessment’’, which will give a link to the available full document on the subject. The expected users of this book are the power engineering students, both at undergraduate and at graduate level, and the engineers in the electric power industry. Many issues related to the reliability of power systems are not included here, because it is not possible to include all the issues of such important and wide field, as it is the power system reliability, in one book. Ljubljana, 10 January 2011

Marko Cˇepin

Acknowledgments

It is very difficult to judge, which of the authors of a scientific work contributed more and which less or to assess which contribution is more valuable. Similarly, it is very difficult to give the recognition they deserve to all the people, who contributed to this book. In certain way, the following colleagues, whose contributions are the most notable, are emphasized. Dr. Andrija Volkanovski helped in discussions about the variants of the power system reliability method and their applications. He developed the power system reliability method as a part of his PhD under my supervision. He is a co-author of Chap. 15, Power system reliability method. The final version of this book has been written much better because of the independent reviewers, who reviewed the writings and contributed with helpful comments and suggestions, which improved the contents of the book. The list of independent reviewers includes: Prof. Dr. Rafael Mihalicˇ, Prof. Dr. Iztok Tiselj, Prof. Dr. Igor Papicˇ, Prof. Dr. Miloš Pantoš, Prof. Dr. Ferdinand Gubina, Asst. Prof. Dr. Ivo Kljenak, Prof. Dr. Tomazˇ Gyergyek, Dr. Andrej Prošek, Dr. Matjazˇ Leskovar, Dr. Mitja Uršicˇ, Blazˇe Gjorgiev, Duško Kancˇev, Martin Draksler, Blazˇ Likovicˇ and Luka Trcˇek. Selected specific parts of specific chapters of this book were prepared with the help of my colleagues and postgraduate students. Duško Kancˇev helped in the preparation of sections about power flow methods. Blazˇe Gjorgiev helped in the preparation of sections about genetic algorithms and simulated annealing. Marko Kolenc helped in the preparation of sections about generating capacity methods. Zˇiva Bricman helped in the preparation of section about blackouts, section about reliability measures and section about event trees. James Cornwell helped in the preparation of section about binary decision diagrams, section about Markov models and section about reliability block diagrams. Gregor Praznik helped in the preparation of section about reliability indices of distribution systems.

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I thank sincerely to all the listed colleagues for their contributions and efforts, which helped me in preparation of this book. I especially thank my own family, Alenka, Katarina and Irena for their understanding and constant encouragement.

Contents

Part I 1

2

Background

Introduction to Power Systems . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Short History of Electric Power Systems . . . . . . . . . . . . . . 1.2.1 People . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Early Power Transmission . . . . . . . . . . . . . . . . . . 1.2.3 Early High-Voltage Systems . . . . . . . . . . . . . . . . 1.2.4 Alternating Current . . . . . . . . . . . . . . . . . . . . . . . 1.2.5 Modern Period . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Consumption and Complexity of Power Systems . . . . . . . . 1.3.1 Electric Automobiles and Other Electric Means of Transport. . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Smart Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 International Thermonuclear Experimental Reactor . 1.4 Objectives of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Problems of Definitions of Reliability . . . . . . . . . . . . . . . . 1.6 Improvement of Reliability of Power Systems . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction to Blackouts . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Selected Recent Blackouts: Causes and Consequences 2.2.1 USA and Canada Blackout, Aug 14, 2003 . . . 2.2.2 Austria Blackout, Aug 27, 2003 . . . . . . . . . . 2.2.3 London Blackout, Aug 28, 2003. . . . . . . . . . 2.2.4 Southern Sweden and Denmark Blackout, Sep 23, 2003 . . . . . . . . . . . . . . . . . . . . . . . 2.2.5 Italian and Swiss Blackout, Sep 28, 2003 . . . 2.2.6 Greece Blackout, July 12, 2004 . . . . . . . . . .

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2.2.7 Moscow Blackout, May 25, 2005 . 2.2.8 Blackout, Nov 4, 2006 . . . . . . . . 2.3 Blackout Prevention . . . . . . . . . . . . . . . . 2.4 Blackout Consequences . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Definition of Reliability and Risk . . . 3.1 Introduction About Terminology 3.2 Reliability and Availability . . . . 3.3 Risk . . . . . . . . . . . . . . . . . . . . 3.4 N - 1 Reliability Criteria . . . . . References . . . . . . . . . . . . . . . . . . . .

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Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Basic Probability Concepts . . . . . . . . . . . . . . . . . 4.4 Theory of Combinations . . . . . . . . . . . . . . . . . . . 4.4.1 Permutations . . . . . . . . . . . . . . . . . . . . . 4.4.2 Combinations . . . . . . . . . . . . . . . . . . . . . 4.5 Conditional Probability and Bayesian Theorem . . . 4.5.1 Conditional Probability . . . . . . . . . . . . . . 4.5.2 Bayes Theorem . . . . . . . . . . . . . . . . . . . 4.6 Random Variables . . . . . . . . . . . . . . . . . . . . . . . 4.7 Probability Distributions . . . . . . . . . . . . . . . . . . . 4.7.1 Normal Distribution or Gauss Distribution or Bell Curve . . . . . . . . . . . . . . . . . . . . . 4.7.2 Lognormal Distribution . . . . . . . . . . . . . . 4.7.3 Beta Distribution . . . . . . . . . . . . . . . . . . 4.7.4 Gamma Distribution . . . . . . . . . . . . . . . . 4.7.5 Uniform Distribution. . . . . . . . . . . . . . . . 4.7.6 Binomial Distribution . . . . . . . . . . . . . . . 4.7.7 Poisson Distribution . . . . . . . . . . . . . . . . 4.7.8 Delta Function Distribution . . . . . . . . . . . 4.7.9 Weibull Distribution . . . . . . . . . . . . . . . . 4.7.10 Exponential Distribution . . . . . . . . . . . . . 4.8 Bathtub Curve . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contents

Part II

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Reliability Methods

Tree Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fault Versus Failure . . . . . . . . . . . . . . . . . . . . . . . . . . Fault Tree Analysis Procedure Steps . . . . . . . . . . . . . . . 5.3.1 Objectives For the Fault Tree Analysis . . . . . . . 5.3.2 Definition of the Top Event of the Fault Tree . . 5.3.3 Definition of the Scope, Resolution, and Rules of the Fault Tree . . . . . . . . . . . . . . . . . . . . . . 5.3.4 Fault Tree Construction. . . . . . . . . . . . . . . . . . 5.3.5 Qualitative Fault Tree Evaluation . . . . . . . . . . . 5.3.6 Preparation of the Probabilistic Failure Database 5.3.7 Quantitative Fault Tree Evaluation . . . . . . . . . . 5.3.8 Interpretation of the Fault Tree Analysis Results 5.4 Applications of the Fault Tree Analysis. . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Event Tree Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Development Procedure. . . . . . . . . . . . . . . . . . . . . . . . 6.3 Plant Familiarization . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Definition of Safety Functions and Event Tree Headings. 6.5 System Success Criteria . . . . . . . . . . . . . . . . . . . . . . . 6.6 Identification of Initiating Events . . . . . . . . . . . . . . . . . 6.7 Definition of Accident Consequences . . . . . . . . . . . . . . 6.8 Determination of Plant Damage State . . . . . . . . . . . . . . 6.9 Event Tree Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . 6.10 Linking of Event Trees With Fault Trees . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7

Binary Decision Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Constucting a Binary Decision Diagram from a Simple Boolean Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Constucting a Binary Decision Diagram from a Truth Table. 7.4 Reducing a Binary Decision Diagram to a More Compact Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Obtaining a Binary Decision Diagram Using Shannon Decomposit...