Risk Assessment of Power Systems E-Book

Wenyuan Li

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: IEEE Press Series on Power Engineering
• Sprache: Englisch

Seitenzahl: 781

Veröffentlichungsjahr: 2014

Beschreibung

Extended models, methods, and applications in power system risk assessment Risk Assessment of Power Systems: Models, Methods, and Applications, Second Edition fills the gap between risk theory and real-world application. Author Wenyuan Li is a leading authority on power system risk and has more than twenty-five years of experience in risk evaluation. This book offers real-world examples to help readers learn to evaluate power system risk during planning, design, operations, and maintenance activities. Some of the new additions in the Second Edition include: * New research and applied achievements in power system risk assessment * A discussion of correlation models in risk evaluation * How to apply risk assessment to renewable energy sources and smart grids * Asset management based on condition monitoring and risk evaluation * Voltage instability risk assessment and its application to system planning The book includes theoretical methods and actual industrial applications. It offers an extensive discussion of component and system models, applied methods, and practical examples, allowing readers to effectively use the basic concepts to conduct risk assessments for power systems in the real world. With every original chapter updated, two new sections added, and five entirely new chapters included to cover new trends, Risk Assessment of Power Systems is an essential reference.

Leseprobe

Table of Contents

IEEE Press

Title page

Copyright page

Dedication

Preface

Preface to the First Edition

1: Introduction

1.1 Risk in Power Systems

1.2 Basic Concepts of Power System Risk Assessment

1.3 Outline of the Book

2: Outage Models of System Components

2.1 Introduction

2.2 Models of Independent Outages

2.3 Models of Dependent Outages

2.4 Conclusions

3: Parameter Estimation in Outage Models

3.1 Introduction

3.2 Point Estimation on Mean and Variance of Failure Data

3.3 Interval Estimation on Mean and Variance of Failure Data

3.4 Estimating Failure Frequency of Individual Components

3.5 Estimating Probability from a Binomial Distribution

3.6 Experimental Distribution of Failure Data and Its Test

3.7 Estimating Parameters in Aging Failure Models

3.8 Conclusions

4: Elements of Risk Evaluation Methods

4.1 Introduction

4.2 Methods for Simple Systems

4.3 Methods for Complex Systems

4.4 Correlation Models in Risk Evaluation

4.5 Conclusions

5: Risk Evaluation Techniques for Power Systems

5.1 Introduction

5.2 Techniques Used in Generation-Demand Systems

5.3 Techniques Used in Radial Distribution Systems

5.4 Techniques Used in Substation Configurations

5.5 Techniques Used in Composite Generation and Transmission Systems

5.6 Conclusions

6: Application of Risk Evaluation to Transmission Development Planning

6.1 Introduction

6.2 Concept of Probabilistic Planning

6.3 Risk Evaluation Approach

6.4 Example 1: Selecting the Lowest-Cost Planning Alternative

6.5 Example 2: Applying Different Planning Criteria

6.6 Conclusions

7: Application of Risk Evaluation to Transmission Operation Planning

7.1 Introduction

7.2 Concept of Risk Evaluation in Operation Planning

7.3 Risk Evaluation Method

7.4 Example 1: Determining the Lowest-Risk Operation Mode

7.5 Example 2: A Simple Case by Hand Calculation

7.6 Conclusions

8: Application of Risk Evaluation to Generation Source Planning

8.1 Introduction

8.2 Procedure of Reliability Planning

8.3 Simulation of Generation and Risk Costs

8.4 Example 1: Selecting Location and Size of Cogenerators

8.5 Example 2: Making a Decision to Retire a Local Generation Plant

8.6 Conclusions

9: Application of Risk Evaluation to Selecting Substation Configurations

9.1 Introduction

9.2 Load Curtailment Model

9.3 Risk Evaluation Approach

9.4 Example 1: Selecting Substation Configuration

9.5 Example 2: Evaluating Effects of Substation Configuration Changes

9.6 Example 3: Selecting Transmission Line Arrangement Associated with Substations

9.7 Conclusions

10: Application of Risk Evaluation to Renewable Energy Systems

10.1 Introduction

10.2 Risk Evaluation of Wind Turbine Power Converter System (WTPCS)

10.3 Risk Evaluation of Photovoltaic Power Systems

10.4 Conclusions

11: Application of Risk Evaluation to Composite Systems with Renewable Sources

11.1 Introduction

11.2 Risk Assessment of a Composite System with Wind Farms and Solar Power Stations

11.3 Determination of Transfer Capability Required by Wind Generation

11.4 Conclusions

12: Risk Evaluation of Wide Area Measurement and Control System

12.1 Introduction

12.2 Hierarchical Structure and Failure Analysis of WAMCS

12.3 Risk Evaluation of Phasor Measurement Units

12.4 Risk Evaluation of Regional Communication Networks in WAMCS

12.5 Risk Evaluation of Backbone Network in WAMCS

12.6 Numerical Results

12.7 Conclusions

13: Reliability-Centered Maintenance

13.1 Introduction

13.2 Basic Tasks in RCM

13.3 Example 1: Transmission Maintenance Scheduling

13.4 Example 2: Workforce Planning in Maintenance

13.5 Example 3: A Simple Case Performed by Hand Calculations

13.6 Conclusions

14: Probabilistic Spare-Equipment Analysis

14.1 Introduction

14.2 Spare-Equipment Analysis Based on Reliability Criteria

14.3 Spare-Equipment Analysis Using the Probabilistic Cost Method

14.4 Example 1: Determining Number and Timing of Spare Transformers

14.5 Example 2: Determining Redundancy Level of 500 kV Reactors

14.6 Conclusions

15: Asset Management Based on Condition Monitoring and Risk Evaluation

15.1 Introduction

15.2 Maintenance Strategy of Overhead Lines

15.3 Replacement Strategy for Aged Transformers

15.4 Conclusions

16: Reliability-Based Transmission-Service Pricing

16.1 Introduction

16.2 Basic Concept

16.3 Calculation Methods

16.4 Rate Design

16.5 Application Example

16.6 Conclusions

17: Voltage Instability Risk Assessment and Its Application to System Planning

17.1 Introduction

17.2 Method of Assessing Voltage Instability Risk

17.3 Tracing and Locating Voltage Instability Risk for Planning Alternatives

17.4 Case Studies

17.5 Conclusions

18: Probabilistic Transient Stability Assessment

18.1 Introduction

18.2 Probabilistic Modeling and Simulation Methods

18.3 Procedure

18.4 Examples

18.5 Conclusions

Appendix A: Basic Probability Concepts

A.1 Probability Calculation Rules

A.2 Random Variable and Its Distribution

A.3 Important Distributions in Risk Evaluation

A.4 Numerical Characteristics

A.5 Nonparametric Kernel Density Estimator

Appendix B: Elements of Monte Carlo Simulation

B.1 General Concept

B.2 Random Number Generators

B.3 Inverse Transform Method of Generating Random Variates

B.4 Important Random Variates in Risk Evaluation

Appendix C: Power Flow Models

C.1 AC Power Flow Models

C.2 DC Power Flow Models

Appendix D: Optimization Algorithms

D.1 Simplex Methods for Linear Programming

D.2 Interior Point Method for Nonlinear Programming

Appendix E: Three Probability Distribution Tables

References

Further Reading

Index

IEEE Press Series on Power Engineering

Copyright © 2014 by The Institute of Electrical and Electronics Engineers, Inc.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Li, Wenyuan, 1946–

Risk assessment of power systems : models, methods, and applications / Wenyuan Li. – Second edition.

pages cm – (Ieee press series on power engineering)

ISBN 978-1-118-68670-6 (hardback)

1. Electric power systems–Reliability–Mathematical models. 2. Electric power failures–Risk assessment. 3. Monte Carlo method. I. Title.

TK1005.L49 2014

621.319'13011–dc23

2013036977

To

Jun and my family

Preface

I am very pleased that the first edition of the book has been well received in both academia and the industry and translated into several languages. Many changes have taken place since the publication of the first edition. The two most influential changes in the power industry are the integration of renewable energy sources into power systems and the progress of smart grids across the world. While green energy sources and innovative technologies in smart grids promote significant opportunities to enhance power systems, they also bring great challenges in power system risk assessment due to additional uncertainties and their probabilistic nature.

Over the last several years, I had a chance to do research in response to the challenges, which resulted in the development of new models, methods, and actual examples. It is necessary to incorporate these developments into the book. I believe that this will attract readers and help them deal with emerging issues of power system risk assessment and management in the tide of changes.

While keeping the concept, structure, and writing style of the first edition, I made some modifications to the original text and added the following new sections and chapters to the second edition:

Correlation models in risk evaluation (Section 4.4)Evaluating risk effects of substation configuration changes (Section 9.5)Application of risk evaluation to renewable energy sources (Chapter 10)Application of risk evaluation to composite systems with renewable sources (Chapter 11)Risk assessment of wide area measurement and control systems (Chapter 12)Asset management based on condition monitoring and risk evaluation (Chapter 15)Voltage instability risk assessment and its application to system planning (Chapter 17).

My special gratitude goes to Dr. Roy Billinton for his consistent advice and assistance. I would like to express my sincere thanks to Drs. Murty Bhavaraju, Lalit Goel, Ruijin Liao, Paul Choudhury, and Ebrahim Vaahedi for their support and encouragement. My appreciation is also extended to Dr. Wijarn Wangdee and my former students, Drs. Juan Yu, Yang Wang, Dabo Zhang, and Zhilong Qin in Chongqing University of China. Some new material added to the second edition is based on the papers that I coauthored with them. Drs. Roy Billinton, Murty Bhavaraju, Lalit Goel and Wijarn Wangdee reviewed the proposal/manuscript of the second edition and provided many valuable suggestions.

I am grateful to IEEE Press and Wiley for their excellent cooperation on this project. In particular, I am thankful to Ms. Mary Hatcher who initiated the idea of the second edition.

I am deeply indebted to my wife, Jun. She always gives me a hand whenever I need help with the book.

Wenyuan Li

Chongqing and Vancouver

September 2013

Preface to the First Edition

The application of power system risk assessment has drawn ever-increasing interests in the electric utility industry, particularly since massive power outage events have happened across the world in recent years. In essence, power systems behave probabilistically and system risk cannot be avoided fully. However, system risk can be evaluated and managed to an acceptable level in planning, design, operation and maintenance activities.

This book originated from my deep involvement in this area, including the development of models and methods and their actual applications. My previous employer, BC Hydro, and current company, British Columbia Transmission Corporation, have always provided me an encouraging atmosphere to carry on many projects for more than 10 years. Practical engineering problems and the deregulation process in the power market have created new challenges in system risk analysis. This enabled me to produce a considerable number of technical reports and papers that formed the foundation of the book. The experience from my academic career to the industrial environment made me recognize that a gap exists between power system risk theory and actual applications in utilities. The intent of this book is to fill that gap. The difficulties faced by practicing engineers include how to determine the component outage models that really reflect reality, how to deal with the uncertainty in statistical data, how to select the appropriate risk evaluation method for a specific case, and particularly, how to apply fundamentals and methodologies to each individual engineering issue.

Graduates who lack an understanding of real utility systems often find themselves at a loss regarding an industrial subject, even if they may have good knowledge of risk theory and basic mathematics. This book has been structured to respond to these concerns. The primary emphasis is placed on the various application topics, although some new models and concepts have been also presented. The majority of examples that demonstrate the applications are based on actual projects that have been performed. This should be the most distinguishing feature of the book. It is my belief that the book will serve both engineers and advanced students who are or will be dedicated to power system risk assessment and management.

The book would not have been possible without my close association with many friends, colleagues, professors, and engineers in the IEEE and the entire power field. My special appreciation goes to Roy Billinton, Yakout Mansour, Ebrahim Vaahedi, and Jerry Korczynski. The papers I coauthored with them are a part of the materials used in the book. Moreover, they have kindly offered me constant support and encouragement in my daily work. My sincere acknowledgement is extended to the following people for their support and help: Gerry Garnett, Don Gillespie, Steven Pai, Narayan Rau, Murty Bhavaraju, Lalit Goel, Bin Shi, Jiaqi Zhou, and Lichun Shu. I would also thank all the individuals whose publications are recorded in the References at the end of the book.

I am also grateful for the cooperation and assistance received from the IEEE Press and John Wiley & Sons Inc., especially Anthony VenGraitis and Lisa Van Horn.

Finally, but never least, I would like to express my deepest gratitude to my wife, Jun, for her sacrifices and patience. She successfully arranged our lives in such a way that I could comfortably work nights and weekends.

Wenyuan Li

Vancouver, Canada

August 2004

1

Introduction

1.1 Risk in Power Systems

There is considerable overlap in the words “risk” and “reliability.” In this book, it is assumed that the two words have identical implications. They are the two facets of the same fact. Higher risk means lower reliability and vice versa. Risk management has wide-ranging content. The intent of this book is to discuss the models, methods, and applications of risk assessment in physical power systems. Risks associated with business, finance, and life safety are not included in the discussion.

The probabilistic behavior of power systems is the root origin of risk. Random failures of system equipment are generally outside the control of power system personnel. Loads always have uncertainties and it is impossible to obtain an exact load forecast. Energy exports and imports under the deregulation environment depend on the volatile power market. Integration of intermittent wind and solar energies into power systems greatly increases the uncertainty in system operation and planning. Applications of information and communication technologies in smart grids introduce more sources of system failure, although these technologies can enhance visualization and controllability of power systems. Consequences of power failures range from electricity interruptions in local areas to a possible widespread blackout. Economic impacts due to supply interruptions are not restricted to loss of revenue by the utility or loss of energy utilization by the customer but include indirect costs imposed on society and environment. Risk assessment has become a challenge and an essential commitment in the power utility industry today.

Risk management includes at least the following three tasks:

1. Performing quantitative risk evaluation

2. Determining measures to reduce risk

3. Justifying an acceptable risk level.

The purpose of quantitative risk evaluation is to create the indices representing system risk. A dictionary definition of risk is “the probability of loss or damage to human beings or assets.” This definition can be used in general cases. However, a comprehensive risk index should contain not only the probability but a combination of probability and consequence. In other words, risk evaluation of power systems should recognize not only the likelihood of failure events but also the severity degree of their consequences. Utilities have dealt with system risks for a long time. The criteria and methods first used in practical applications were all deterministically based, such as the percentage reserve in generation capacity planning and the single contingency principle in transmission planning. The deterministic criteria have served the power industry for years. The basic weakness is that they do not respond to the probabilistic nature of power system behavior, load variation, and component failures.

A measure to reduce system risk is generally associated with enhancement of the system. In order to determine a rational measure, both the impact of the measure on risk reduction and the cost needed to implement it should be quantified. A probabilistic economic analysis is usually required. In risk management, an important concept to be appreciated is that zero risk can never be reached since random failure events are uncontrollable. In many cases, a decision has to be made to accept a risk as long as it can be technically and financially justified. Selecting a rational measure to reduce risks or accepting a risk level is a decision-making process. It should be recognized that on the one hand, quantitative risk evaluation is the basis of this process, and on the other hand, the process is more than risk evaluation and requires technical, economic, societal, and environmental assessments.

The risk assessment of power systems can be applied to all the areas in electric power utilities, including:

Quantified risk evaluation in generation, transmission, substation, distribution, communication, and control systemsProbabilistic security assessmentProbabilistic criteria in system planning and operationCompromise between system risk and economic benefit in a decision-making processRisk assessment of renewable energy systemsRisk assessment of communication networks and smart gridsEquipment aging failure managementSpare equipment strategyReliability-centered maintenance and asset managementLoad side risk managementPerformance-based rate policyOperation-risk monitoringInterruption damage cost assessment.

Risk management and quantified risk assessment have become increasingly important since the power industry entered the deregulation era. The new competition environment forces utilities to plan and operate their systems closer to the limit. The stressed operation conditions have led to deterioration in system reliability. In fact, a lot of power outage events have occurred across the world in the past few years. According to an EPRI (Electric Power Research Institute) report based on the national survey in all business sectors, the U.S. economy alone is losing between $104 and $164 billion a year due to power system outages [1]. Severe power outage events happen from time to time. For instance, a major system disturbance separated the Western Electricity Coordinating Council (WECC) system in the west of North America into four islands on August 10, 1996, interrupting the electricity service to 7.5 million customers for a period of up to nine hours. The 1998 blackout at the Auckland central business district in New Zealand impacted 30 square blocks of the downtown area for about two months, resulting in a lawsuit totaling $600 million against the utility. On August 14, 2003, the massive blackout in the east of North America covered eight states in United States and two provinces in Canada, bringing about 50 million people into darkness for periods ranging from one to several days. On August 18, 2005, multiple power plants were kicked off due to an imbalanced power grid in Indonesia, leaving about 100 million people in darkness up to five hours. In November 2006, a high voltage line switching action triggered massive power outages for 10 million people in Germany, France, Italy, and Spain. On November 10, 2009, storms caused cascading outages that cut power to 60 million people in Brazil for three hours and 7 million people in Paraguay. On July 30 and 31, 2012, the two worst outages hit the power grids in India, leaving 370 and 670 million people without power, respectively. These severe power outages let us realize that the single contingency criterion (the N−1 principle) that has been used for many years in the power industry may not be sufficient to preserve a reasonable system reliability level. However, it is also commonly recognized that no utility can financially justify the N−2 or N−3 principle in power system planning. Obviously, one alternative is to bring risk management into the practice in planning, design, operation, and maintenance, keeping system risk within an acceptable range. On the other hand, the customers of the power industry become more and more knowledgeable about electric power systems. They understand that it is impossible to expect 100% continuity in power supply without any risk of outages. However, they have the right to know the risk level, including information on how often, for how long, and how severely a power interruption event can happen to them on the average. To answer this question is one of the objectives of power system risk assessment.

1.2 Basic Concepts of Power System Risk Assessment

1.2.1 System Risk Evaluation

Power system risk evaluation is generally associated with the following four tasks:

1. Determining component outage models

2. Selecting system states and calculating their probabilities

3. Evaluating the consequences of selected system states

4. Calculating risk indices.

A power system consists of many components, including generators, transmission lines, cables, transformers, breakers, switches, reactive power source equipment, and devices of protection, control, and communication networks. Component outages are the root cause of a system failure state. The first task in system risk evaluation is to determine component outage models. Component outages are classed into two categories: independent and dependent outages. Each category can be further classified according to the outage modes. In most cases, only repairable forced outages are considered, whereas in some cases, planned outages are also modeled. Aging failures are not incorporated into traditional risk evaluation. This book presents a modeling approach of aging failures and demonstrates examples of its application.

The second task is to select system failure states and calculate their probabilities. There are two basic methods for selecting system states: state enumeration and Monte Carlo simulation. Both methods have merits and demerits. In general, if complex operating conditions are not considered and/or the failure probabilities of components are quite small, state enumeration techniques are more efficient. When complex operating conditions are involved and/or the number of severe events is relatively large, Monte Carlo methods are often preferable.

The third task is to perform the analysis for system failure states and assess their consequences. Depending on the system under study, the analysis could be associated with simple power balance, connectivity identification of a network configuration, or a complex calculation process including power flow, optimal power flow, or even transient and voltage stability evaluation.

Calculating risk indices is the fourth task. As mentioned earlier, risk is a combination of probability and consequence. With the information obtained in the second and third task, an index that truly represents system risk can be created. There are many possible risk indices for different purposes. Most of them are basically the expected value of a random variable, although a probability distribution can be calculated in some cases. It is important to appreciate that the expected value is not a deterministic parameter. It is the long-run average of phenomena under study. The expected indices serve as the risk indicators that reflect various factors, including component capacities and outages, load profiles and forecast uncertainties, system configurations and operational conditions, and so on.

According to system state analysis, power system risk assessment can be divided into two basic aspects: system adequacy and system security. Adequacy relates to the existence of sufficient facilities within the system to satisfy consumer load demands and system operational constraints. Adequacy is therefore associated with the static conditions that do not include system dynamic and transient processes. Security relates to the ability of the system to respond to dynamic and transient disturbances arising within the system. Security is therefore associated with the response of the system to whatever perturbations it is subject to. Normally, security evaluation requires the analysis of dynamic, transient, or voltage stability in the system. It should be pointed out that most of the risk evaluation techniques that have been used in actual applications of utilities are in the domain of adequacy assessment. Some ideas for security assessment have been addressed recently. However, practical application in this area is still limited compared with adequacy assessment. It should be noted that most risk indices used in risk evaluation are inadequacy indices, not overall risk indices. The system indices that are based on historical outage statistics encompass the effect of both inadequacy and insecurity. It is important to recognize this fundamental difference in actual engineering applications.

A power system includes the three fundamental functions of generation, transmission (including substation), and distribution. Traditionally, the three functional zones are included in one utility. As reform in the power industry proceeds, the three functional zones have been gradually separated to form organizationally independent generation, transmission, and distribution companies in many countries. In either case, risk assessment can be, and is, conducted in each of these functional zones. The risk evaluation for an overall system, including generation, transmission, and distribution, is impractical because such a system is too enormous to handle in terms of existing computing capacity and accuracy requirements. On the one hand, calculation modeling and algorithms are quite different for the risk evaluations of generation, or transmission, or substation, or distribution systems. On the other hand, many techniques have been successfully developed to perform risk evaluation for composite generation and transmission systems or composite transmission and substation systems. In the case of a large scale transmission system, it is reasonable to limit the study to an area or subsystem. Doing so can provide more realistic results than evaluating the whole system. This is due to the fact that a change or reinforcement in the network may considerably affect a local area but have little impact on remote parts of the system. The contribution to the overall reliability of a large system due to a local line addition or reconfiguration may be so small that it is masked by computational errors and, consequently, cannot be reflected in the risk change of the whole system. This contribution, however, can be a relatively large proportion of the risk change in the local area.

Smart grid is a power system with high penetration of renewable energy sources (wind, solar, and others) and integration of information technologies and communication networks. In addition to renewable sources, other new components in the context of smart grid include phasor measurement units, wide area measurement and control system, condition monitoring, advanced asset management, microgrids, smart metering, electric vehicles, and so on. Risk evaluation of smart grid must establish the outage models associated with renewable resources, new technologies, new devices, and communication networks. On the one hand, the basic concepts and theories of risk assessment are still valid. On the other hand, these concepts and theories must be extended to capture the features of the new components.

Generally, it is necessary to assess the relative benefits between different alternatives, including the option of doing nothing. The level of analysis need not be any more complex than that which enables the relative merits to be assessed. The ability to include a high degree of precision in calculations should never override the inherent uncertainty in the data. An absolute risk index, although an ideal objective, is virtually impossible to evaluate. This does not weaken the necessity to objectively assess the relative merits of alternative schemes. This is an important point to be appreciated in power system risk evaluation.

1.2.2 Data in Risk Evaluation

The reliability data required in power system risk evaluation are the parameters of component outage models. They are basically calculated from historical statistics, although an engineering judgment based on individual equipment assessment is also used in some special cases. With advancement of equipment-condition monitoring technologies in recent years, making use of condition monitoring measurements to more accurately estimate component outage parameters has become a new idea. Collecting suitable data is at least as essential as developing risk evaluation methods.

The data requirements should reflect the need for risk assessments. The data must be sufficiently comprehensive to ensure that an evaluation method can be applied, but restrictive enough to ensure that unnecessary data are not collected. For simple models, data relate to two main processes of component behavior, namely, the failure process and the restoration process. For more complex models, data are associated with transition rates between various states considered.

The quality of data is an important factor to consider in data collection. The usual saying of “garbage in, garbage out” refers to the fact that if the quality of data cannot be guaranteed, risk evaluation results would not make any sense. Outage statistics and equipment-condition monitoring measurements constitute a huge data pool and some bad or invalid records cannot be fully avoided in any database. Data processing is necessary to filter out bad data. A parameter estimation procedure is needed to acquire the input data of risk evaluation from raw statistics. This requires the suitable design of statistical data modeling.

Another characteristic of reliability data is its dynamic feature. The volume of outage records will increase over years and, therefore, the average failure frequency and repair time for a piece of equipment or an equipment group will change from year to year. The reliability database should have a means of continuous updating and should be also flexible enough to output reports in a variety of formats. Figure 1.1 shows an example of reliability data collection system.

Figure 1.1 Reliability data collection system. SETR, system equipment trouble report.

1.2.3 Unit Interruption Cost

The basic function of a modern electric power system is to provide electric energy to its customers at the lowest possible cost and at an acceptable risk level. There is a conflict between economy and risk. Risk cost evaluation is an appropriate approach to putting risk and economic factors on a unified scale of monetary value [2].

The risk cost can be evaluated using a unit energy interruption cost multiplied by expected energy not supplied. However, quantification of the interruption cost is complex. The customer damage functions that are based on customer surveys have been presented for years. Although this method is applied in risk evaluation, there have been a lot of debates about its use. One typical viewpoint is that the customer damage functions do not represent utility damages and it is inappropriate to use them to balance the capital investment of a utility. The opposite argument is that customers eventually pay all costs through rates and, thus, the customer's interruption cost should be considered in utility system planning. This is a complicated issue that relies on many nontechnical aspects, including regulation or deregulation, ownership, and rate design.

Three methods of evaluating the unit interruption cost are discussed here. Different utilities may select a different method in their practice and studies.

1. Method based on customer damage functions. A customer damage function is obtained from customer surveys and relevant statistic analysis. Based on a wide investigation of utility companies across Canada, for instance, the average unit interruption cost is between $4/KWh (kilowatt hour) and $10/KWh. This is the average social damage cost due to electricity supply interruptions. It is important to recognize that the unit interruption cost is region-, country-, and system-specific. A utility should use the unit interruption cost that is based on its own customer survey and system analysis. This method has a general implication and is particularly well suited to the utility with a customer-focused strategy.

2. Method based on capital investments. For a utility, any capital investment to reinforce the power system brings about an incremental decrease in system risk. In other words, there is a quantifiable relationship between the capital investment and the system risk index. With considerable studies in system reinforcement projects and relevant system risk assessments, the average unit interruption cost that is based on the capital investments can be obtained. The details of the method will be discussed in Chapter 16. This method may be particularly preferred by a private utility.

3. Method based on gross domestic product. A simple and useful method is to use the gross domestic product (GDP) concept. The gross domestic product for a province, state, or country divided by the total annual electric energy consumption of the province, state, or country results in a dollar value per KWh. This number reflects the average economic damage cost due to one KWh of electric energy loss in that province, state, or country. Obviously, this method is suitable to a utility owned by a government since the overall economic benefit in the province, state, or country must be considered as a whole picture.

1.3 Outline of the Book

Considerable efforts have been devoted to power system risk assessment in the past decades. There are many technical papers and several books in this area [3, 4–9, 10, 11]. The majority of the books have focused on analytical techniques [4, 6–9] and one book has focused on Monte Carlo simulation methods [3]. The emphasis in these books is placed on the theory and general methods for power system reliability evaluation. Similar to Reference 5, this book emphasizes actual applications in the industry environment with the following features:

Most of this book is devoted to practical applications. The topics addressed are the actual issues in the utility industry. The special concepts, methods, models, and procedures for the different applications in planning, operation, maintenance, and asset management are developed, including those associated with renewable sources, smart grids, equipment-condition monitoring, and system security risk. The majority of the examples are from real utility systems. The results in the applications have been implemented in utilities' projects.Outage models of system components are systematically discussed in Chapter 2. Some concepts are new, such as semiforced outage, individual model for common cause outage, cascading outage, and aging failure modeling. Condition monitoring-based models are presented in Chapter 15 and applied in the power system risk assessment for the first time.One whole chapter (Chapter 3) is committed to the parameter estimation of component outage models. This is an issue associated with how to perform statistical processing for historical outage records to handle the uncertainty of input data in risk assessments.In evaluation methods, both analytical and Monte Carlo approaches are discussed, with an emphasis on applied techniques and actual considerations in generation, transmission, substation, distribution, and wide area measurement and control systems (WAMCS). The methods that are not popular in practical applications are not included.

The book can be divided into three parts. The first part is the models and methods that are presented in Chapters 2–5. The second part, including Chapters 6–18, focuses on the topics in practical applications. The third part consists of five appendices, which provide the background knowledge needed in power system risk assessment.

Chapters 2 and 3 discuss modeling and data issues at the system component level. Chapter 2 presents the outage models of system components, including various independent and dependent outages. These are the basis of system risk evaluation. Chapter 3 discusses the estimation methods of the parameters used in component outage models. These include the point and interval estimations of failure data, experimental distributions of failure statistics, and parameter estimation in aging failure models. The essence of parameter estimation is determination of input data in risk evaluation. This is one of the key steps toward actual applications.

Chapters 4 and 5 discuss the evaluation methods and analysis techniques for overall systems. Chapter 4 summarizes the general risk evaluation methods that have been extensively applied in power system risk assessment. The probability convolution, series and parallel networks, minimum cutsets, Markov equations, and frequency-duration approaches for simple systems are described first, and then emphasis is placed on the state enumeration and Monte Carlo simulation methods for complex systems. The correlation models in risk evaluation are introduced as a new section in this edition. The merits and limitations of different methods are discussed from a viewpoint of practical engineering application.

Chapter 5 illustrates the risk evaluation methods for generation, distribution, substation, and transmission systems using both Monte Carlo simulation and state enumeration techniques. The focus is placed on the approaches of selecting system states and the techniques of performing system analyses. Practical considerations in applications are discussed. The formulas of risk indices for generation, distribution, substation, and transmission systems are derived.

Applied topics are presented in Chapters 6–18. These cover a variety of areas in planning, operation, maintenance, and asset management, including the applications in renewable sources, smart grids (PMU and WAMCS), and system security. In each chapter, not only are the concept, method, and procedure for a specific application described, but examples are also given to demonstrate the details of each application. The majority of the applications are based on actual projects in the utility industry.

Chapter 6 illustrates the application of risk assessment to transmission development planning. After concepts and approaches are discussed, two examples are provided. The first one shows how to select the lowest cost planning alternative and the second one explains how to apply different planning criteria.

Chapter 7 addresses the application of risk assessment to transmission operation. The special aspects associated with operation modes are discussed. These include the impacts on system risk of load transfers, generation pattern changes, network reconfigurations, and switching actions. In addition to an example of determining the lowest risk operation mode in a large, actual system, a simple case of using hand calculations is also given to demonstrate the procedure in detail.

Chapter 8 discusses the application of risk assessment to generation source planning. The basic concepts and methods for generation reliability planning under network constraint conditions are explained. Two examples are provided. One is associated with determination of location and size of cogeneration and the other one is associated with decision making on the retirement of a local generation plant in a utility.

Chapter 9 presents the application of risk assessment to selecting substation or subtransmission system configurations. The general method for risk evaluation in a combined system of substations and transmission network is developed. Three examples are given to illustrate how to apply the presented method in selecting the best substation configuration under transmission network constraints, evaluating the effects of substation configuration changes (a new section in this edition), and determining the optimal transmission line arrangement connected to several substation configurations, respectively.

Chapter 10, as a new chapter in this edition, presents the risk parameter models and risk evaluation methods for renewable sources using wind turbine power converter system and photovoltaic power system as two applications. Renewable energy sources (wind and solar energies) have been increasingly integrated into power systems in recent years. Adding risk evaluation methods for renewable sources to this edition is necessary and timely. This topic is covered by two chapters, with Chapter 10 focusing on individual renewable source generating systems and Chapter 11 focusing on the impact analysis of multiple renewable sources on the risk evaluation and probabilistic planning of a composite system.

Chapter 11 is a new chapter for the application of risk evaluation to composite systems with renewable sources. There are two subtopics. Section 11.2, subtitled “Risk Assessment of Composite System with Wind Farms and Solar Power Stations,” is focused on the method of modeling both randomness and correlation in a mixed wind-solar system, whereas Section 11.3, subtitled “Determination of Transfer Capability Required by Wind Generation,” is an application of the risk evaluation method to an actual planning issue for a wind-generation integrated system in a utility.

Chapter 12 is a new chapter in which the risk evaluation of a wide area measurement and control system (WAMCS) in smart grid is presented for the first time. This chapter systematically addresses the risk evaluation methods of WAMCS, including the models and techniques to quantify the risks of phasor measurement units (PMUs), regional communication networks, and backbone communication networks.

In Chapter 13, reliability-centered maintenance is discussed. The application of risk assessment in this area has a wide range of implications. Following the discussion on basic tasks in reliability-centered maintenance, three examples are provided. The first one is determination of the lowest risk maintenance scheduling. The second addresses the issue of work force planning in maintenance. The third shows that a reliability-centered maintenance problem in real life does not always have to be complex and can be solved through simple calculations in some cases.

In Chapter 14, probabilistic spare equipment planning is addressed. This area has been a challenge in the electric power industry for years. The spare equipment issue is tightly related to equipment aging and thus the aging failure mode has to be considered. The spare equipment analysis methods based on risk criteria and probabilistic cost models are presented. Two practical applications from utility projects are discussed in detail. In the first one, the number and timing of spare transformers are determined, and in the second one, online redundancy of 500 kV reactors is analyzed.

Chapter 15 is a new chapter discussing asset management based on both condition monitoring and risk evaluation. In the traditional risk evaluation, failure data of system components are obtained from historical failure statistics. As equipment-condition monitoring technologies are applied in smart grid, condition monitoring provides accurate information of equipment status. Combining equipment-condition monitoring with risk evaluation becomes a new idea in asset management. This chapter presents two applications: the maintenance strategy of nonaged overhead line and the replacement strategy of an aged transformer. Both are based on equipment-condition monitoring and system risk evaluation.

Chapter 16 discusses the special application of risk assessment in reliability-based transmission service pricing. In the deregulation environment of the power industry, system reliability becomes part of transmission services and must be reflected in price designs. The basic concept, calculation method, and rate design based on quantified system risk evaluation are illustrated. A utility example is used to explain the application.

Chapter 17, a new chapter, addresses voltage instability risk assessment and its application to system planning. Probabilistic security assessment has been a challenge in the risk evaluation area. The basic method for assessing voltage instability risk is proposed first, and then an application to tracing and locating voltage instability risk for planning alternatives is presented with case studies.

Chapter 18 presents probabilistic transient stability assessment. This is a relatively immature area in power system risk evaluation. The failure models and simulation methods associated with transient stability are addressed. A utility system is used as an example in which two applications are discussed. One is associated with the calculation of probabilistic transfer limit and the other with the determination of probabilistic generation rejection requirements.

There are five appendices in total. Appendices A and B contain the mathematical knowledge for risk assessment. Appendix A provides basic probability concepts and Appendix B presents the elements of Monte Carlo simulation. Appendices C and D give the fundamentals of power flow models and optimization algorithms, respectively, that are used in power system risk assessment. Appendix E provides the three probability distribution tables that are often utilized in parameter estimation.

This edition of the book provides the extensive new contents for risk assessments associated with renewable sources, smart grid, WAMCS, equipment-condition monitoring, and voltage instability. However, it still does not pretend to include all the known and available materials on the subject. Instead, it focuses on the aspects that have not been but should be sufficiently addressed in power system risk assessment. It is believed that the book will enable a reader who lacks experience in the power utility industry, such as a university student, to gain practical ideas required in performing risk assessment of real power systems. It will also enable a reader who wants to learn more about modeling and methods and to apply them to solving actual problems, such as an engineer, to acquire the requisite expertise in power system risk assessment.

2

Outage Models of System Components

2.1 Introduction

This chapter systematically discusses the outage models of system components. A power system consists of various components, such as generators, lines, cables, feeders, transformers, breakers, switches, reactors, and capacitors. Generally, component outages can be divided into two categories: independent and dependent. Models of independent outages are described in Section 2.2 and those of dependent outages in Section 2.3.

The category of independent outages can be further classified. There are different classification methods. They can be classed as forced, semiforced, and planned outages in terms of outage nature, or as full and partial failures in accordance with failure states. Forced failures are generally distinguished as repairable and nonrepairable failures. Considerable failures are repairable, whereas nonrepairable failures also often take place in real life. Equipment aging is a general phenomenon and has gradually become a major concern in many utilities. Therefore the aging failure mode of components should be incorporated in risk evaluation when components approach the end of their lives. In the traditional risk evaluation of power systems, only repairable failures are considered and aging failures are ignored. Excluding aging failures will most likely result in underestimation of power system risk. This book treats aging failure modeling as one of its main focuses.

There are different dependent outages. A simultaneous failure of two overhead lines on the same tower due to lightning is a typical example. This type of failure has been called a common cause failure. Any failure of terminal equipment at a substation may cause multiple line outages. An adverse weather condition or a major storm disaster greatly increases the failure possibility of all components exposed to it. Protection coordination in power systems causes a chance of cascading outages, although it also plays an important role in system security and safety. All these dependent outages generally produce much more severe consequences than independent outages. Major power outages and blackouts have historically been associated with dependent outage events.