4»IEEE POWER SYSTEMS .*ISK ASSESSMENT OF. Models, Methods, and Applications. Wiley. Ph.D., Fellow, IfE, CAE, EIC SECOND EDITION

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1 .*ISK ASSESSMENT OF POWER SYSTEMS Models, Methods, and Applications SECOND EDITION Wenyuan Li, Ph.D., Fellow, IfE, CAE, EIC Chongqing University, China BC H> Canada, n IEEE PRESS SERIES ON POWER ENGINEERING 4»IEEE IEEE PRESS Wiley

2 Preface XIX Preface to the First Edition xxi 1 Introduction Risk in Power Systems / Basic Concepts of Power System Risk Assessment / System Risk Evaluation / Data in Risk Evaluation / Unit Interruption Cost / Outline of the Book / 9 2 Outage Models of System Components Introduction / Models of Independent Outages / Repairable Forced Failure / Aging Failure / Nonrepairable Chance Failure / Planned Outage / Semiforced Outage / Partial Failure Mode / Multiple Failure Mode / Models of Dependent Outages / Common-Cause Outage / Component-Group Outage / Station-Originated Outage / Cascading Outage / Environment-Dependent 2.4 Conclusions / 42 Failure / 40 vii

3 Parameter Estimation in Outage Models Introduction / Point Estimation on Mean and Variance of Failure Data / Sample Mean / Sample Variance / Interval Estimation on Mean and Variance of Failure Data / General Concept of Confidence Interval / Confidence Interval of Mean / Confidence Interval of Variance / Estimating Failure Frequency of Individual Components / Point Estimation / Interval Estimation / Estimating Probability from a Binomial Distribution / Experimental Distribution of Failure Data and Its Test / Experimental Distribution of Failure Data / Test of Experimental Distribution / Estimating Parameters in Aging Failure Models / Mean Life and Its Standard Deviation in the Normal Model / Shape and Scale Parameters in the Weibull Model / Example / Conclusions / 70 Elements of Risk Evaluation Methods Introduction / Methods for Simple Systems / Probability Convolution / Series and Parallel Networks / Minimum Cutsets / Markov Equations / Frequency-Duration Approaches / Methods for Complex Systems / State Enumeration / Nonsequential Monte Carlo Simulation / Sequential Monte Carlo Simulation / Correlation Models in Risk Evaluation / Correlation Measures / Correlation Matrix Methods / Copula Functions / Conclusions / 102

4 ix 5 Risk Evaluation Techniques for Power Systems Introduction / Techniques Used in Generation-Demand Systems / Convolution Technique / State Sampling Method / State Duration Sampling Method / Techniques Used in Radial Distribution Systems / Analytical Technique / State Duration Sampling Method / Techniques Used in Substation Configurations / Failure Modes and Modeling / Connectivity Identification / Stratified State Enumeration Method / State Duration Sampling Method / Techniques Used in Composite Generation and Transmission Systems / Basic Procedure / Component Failure Models / Load Curve Models / Contingency Analysis / Optimization Models for Load Curtailments / State Enumeration Method / State Sampling Method / Conclusions / Application of Risk Evaluation to Transmission Development Planning Introduction / Concept of Probabilistic Planning / Basic Procedure / Cost Analysis / Present Value / Risk Evaluation Approach / Risk Evaluation Procedure / Risk Cost Model / Example 1: Selecting the Lowest-Cost Planning System Description / Planning Alternatives / Risk Evaluation / Overall Economic Analysis / Summary / 157 Alternative / 149

5 X CONTENTS 6.5 Example 2: Applying Different Planning Criteria / System and Planning Alternatives / Study Conditions and Data / Risk and Risk Cost Evaluation / Overall Economic Analysis / Summary / Conclusions / Application of Risk Evaluation to Transmission Operation Planning Introduction / Concept of Risk Evaluation in Operation Planning / Risk Evaluation Method / Example 1: Determining the Lowest-Risk Operation Mode / System and Study Conditions / Assessing Impacts of Load Transfer / Comparing Different Reconfigurations / Selecting Operation Mode under the N 2 Condition / Summary / Example 2: A Simple Case by Hand Calculation / Basic Concept / Case Description / Study Conditions and Data / Risk Evaluation / Summary / Conclusions / Application of Risk Evaluation to Generation Source Planning Introduction / Procedure of Reliability Planning / Simulation of Generation and Risk Costs / Simulation Approach / Minimization Cost Model / Expected Generation and Risk Costs / Example 1: Selecting Location and Size of Cogenerators / Basic Concept / System and Cogeneration Risk Sensitivity Analysis / Maximum Benefit Analysis / Summary / 205 Candidates / 197

6 Xi 8.5 Example 2: Making a Decision to Retire a Local Generation Plant / Case Description / Risk Evaluation / Total Cost Analysis / Summary / Conclusions / Application of Risk Evaluation to Selecting Substation Configurations Introduction / Load Curtailment Model / Risk Evaluation Approach / Component Failure Models / Procedure of Risk Evaluation / Economic Analysis Method / Example 1: Selecting Substation Configuration / Two Substation Configurations / Risk Evaluation / Economic Analysis / Summary / Example 2: Evaluating Effects of Substation Configuration Changes / Simplified Model for Evaluating Substation Configurations / Problem Description / Risk Evaluation / Summary / Example 3: Selecting Transmission Line Arrangement Associated with Substations / Description of Two Options / Risk Evaluation and Economic Analysis / Summary / Conclusions / Application of Risk Evaluation to Renewable Energy Systems Introduction / Risk Evaluation of Wind Turbine Power Converter System (WTPCS) / Basic Concepts / 237

7 Xii CONTENTS Power Losses and Temperatures Components / 238 of WTPCS Risk Evaluation of WTPCS / Case Study / Summary / Risk Evaluation of Photovoltaic Power Systems / Two Basic Structures of Photovoltaic Power Systems / Risk Parameters of Photovoltaic Inverters / Risk Evaluation of Photovoltaic Power System / Case Study / Summary / Conclusions / Application of Risk Evaluation to Composite Systems with Renewable Sources Introduction / Risk Assessment of a Composite System with Wind Farms and Solar Power Stations / Probability Models of Renewable Sources and Bus Load Curves / Multiple Correlations among Renewable Sources and Bus/Regional Loads / Risk Assessment Considering Multiple Correlations / Case Study / Summary / Determination of Transfer Capability Required by Wind Generation / System, Conditions, and Method / Wind Generation Model / Equivalence of Wind Power in Generation Systems / Transfer Capability Required by Summary / Conclusions / 310 Wind Generation / Risk Evaluation of Wide Area Measurement and Control System Introduction / Hierarchical Structure and Failure Analysis of WAMCS / Hierarchical Structure of WAMCS / Failure Analysis Technique for WAMCS / 315

8 Xiii 12.3 Risk Evaluation of Phasor Measurement Units / Markov State Models of PMU Modules / Equivalent Two-State Model of PMU / Risk Evaluation of Regional Communication Networks in WAMCS / Classification of Regional Communication Networks / Survival Mechanisms of Regional Networks / Risk Evaluation in Two Survival Mechanisms / Equivalent Two-State Model of a Regional Communication Network / Risk Evaluation of Backbone Network in WAMCS / Equivalent Risk Model of Backbone Communication Network / Risk Evaluation of Optic Fiber System / Numerical Results / Risk Indices of PMU / Risk Indices of Regional Communication Networks / Risk Indices of the Backbone Communication Network / Risk Indices of Overall WAMCS / Conclusions / 349 Reliability-Centered Maintenance Introduction / Basic Tasks in RCM / Comparison between Maintenance Alternatives / Lowest-Risk Maintenance Scheduling / Predictive Maintenance versus Corrective Maintenance / Ranking Importance of Components / Example 1: Transmission Maintenance Scheduling / Procedure of Transmission Maintenance Planning / Description of the System and Maintenance Outage / The Lowest-Risk Schedule of the Cable Replacement / Summary / Example 2: Workforce Planning in Maintenance / Problem Description / Procedure / Case Study and Results / Summary / 363

9 XiV CONTENTS 13.5 Example 3: A Simple Case Performed by Hand Calculations / Case Description / Study Conditions and Data / EENS Evaluation / Summary / Conclusions / Probabilistic Spare-Equipment Analysis Introduction / Spare-Equipment Analysis Based on Reliability Unavailability of Components / 370 Criteria / Group Reliability and Spare-Equipment Analysis / Spare-Equipment Analysis Using the Probabilistic Cost Method / Failure Cost Model / Unit Failure Cost Estimation / Annual Investment Cost Model / Present Value Approach / Procedure of Spare-Equipment Analysis / Example 1: Determining Number and Timing of Spare Transformers / Transformer Group and Data / Spare-Transformer Analysis Based on Group Failure Probability / Spare-Transformer Plans Based on the Probabilistic Cost Model / Summary / Example 2: Determining Redundancy Reactors / Problem Description / Study Conditions and Data / Redundancy Analysis / Summary / Conclusions / 387 Level of 500 kv 15 Asset Management Based on Condition Monitoring and Risk Evaluation Introduction / Maintenance Strategy of Overhead Lines / Risk Evaluation Using Condition Monitoring Data / Overhead Line Maintenance Strategy / 397

10 XV Case Study / Summary / Replacement Strategy for Aged Transformers / Transformer Aging Failure Unavailability Using Condition Monitoring Data / Transformer Replacement Strategy / Case Study / Summary / Conclusions / Reliability-Based Transmission-Service Pricing Introduction / Basic Concept / Incremental Reliability Value / Impacts of Customers on System Reliability / Reliability Component in Price Design / Calculation Methods / Unit Incremental Reliability Value / Generation Credit for Reliability Improvement / Load Charge for Reliability Degradation / Load Charge Rate Due to Generation Credit / Rate Design / Charge Rate for Wheeling Customers / Charge Rate for Native Customers / Credit to Generation Customers / Application Example / Calculation of the UIRV / Calculation of the GCRI / Calculation of the LCRD / Calculation of the LCRGC / Calculations of Charge Rates / Conclusions / Voltage Instability Risk Assessment and Its Application to System Planning Introduction / Method of Assessing Voltage Instability Risk / Maximum Loadability Model for System States / Models for Identifying Weak Branches and Buses / 436 States / Determination of Contingency System Procedure of Calculating Voltage Instability Risk Indices / 444

11 XVI CONTENTS 17.3 Tracing and Locating Voltage Instability Risk for Planning Alternatives / Case Studies / Results of the IEEE 14-Bus System / Results of the 171-Bus Utility System / Conclusions / Probabilistic Transient Stability Assessment Introduction / Probabilistic Modeling and Simulation Methods / Selection of Pre-Fault System States / Fault Models / Monte Carlo Simulation of Fault Events / Transient Stability Simulation / Procedure / Procedure for the First Type of Study / Procedure for the Second Type of Study / Examples / System Description and Data / Transfer Limit Calculation in the Columbia River System / Generation Rejection Requirement in the Peace River System / Summary / Conclusions / 475 Appendix A Basic Probability Concepts 477 A.l Probability Calculation Rules / 477 A.1.1 Intersection / 477 A.1.2 Union / 477 A. 1.3 Full Conditional Probability / 478 A.2 Random Variable and Its Distribution / 478 A.3 Important Distributions in Risk Evaluation / 479 A.3.1 Exponential A.3.2 Normal Distribution / 479 Distribution / 479 A.3.3 Log-Normal A.3.4 Weibull Distribution / 481 Distribution / 481 A.3.5 Gamma Distribution / 482 A.3.6 Beta Distribution / 483 A.4 Numerical Characteristics / 483 A.4.1 Mathematical Expectation / 483 A.4.2 Variance and Standard Deviation / 484 A.4.3 Covariance and Correlation Coefficients / 484

12 xvii A.5 Nonparametric Kernel Density Estimator / 485 A.5.1 Basic Concept / 485 A.5.2 Determination of the Bandwidth / 486 Appendix B Elements of Monte Carlo Simulation 489 B.l General Concept / 489 B.2 Random Number Generators / 490 B.2.1 Multiplicative Congruent Generator / 490 B.2.2 Mixed Congruent Generator / 491 B.3 Inverse Transform Method of Generating Random Variates / 491 B. 4 Important Random Variates in Risk Evaluation / 492 B.4.1 Exponential Distribution Random Variate / 492 B.4.2 Normal Distribution Random Variate / 493 B.4.3 Log-Normal Distribution Random Variate / 494 B.4.4 Weibull Distribution Random Variate / 494 B.4.5 Gamma Distribution Random Variate / 495 B. 4.6 Beta Distribution Random Variate / 495 Appendix C Power Flow Models 497 C. l AC Power Flow Models / 497 C. 1.1 Power Flow Equations / 497 C.1.2 Newton-Raphson Method / 497 C.1.3 Fast Decoupled Method / 498 C. 2 DC Power Flow Models / 499 C.2.1 Basic Equation / 499 C.2.2 Line Flow Equation / 500 Appendix D Optimization Algorithms 503 D. l Simplex Methods for Linear Programming / 503 D. 1.1 Primal Simplex Method / 503 D.1.2 Dual Simplex Method / 505 D.2 Interior Point Method for Nonlinear Programming / 506 D.2.1 Optimality and Feasibility Conditions / 506 D.2.2 Procedure of the Algorithm / 508 Appendix E Three Probability Distribution Tables 511 References 515 Further Reading 523 Index 525

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