Risk Assessment of Power Systems: Models, Methods, and Applications(IEEE Press Series on Power and Energy Systems)

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.

Table of Contents:
Preface xix Preface to the First Edition xxi 1 Introduction 1 1.1 Risk in Power Systems 1 1.2 Basic Concepts of Power System Risk Assessment 4 1.2.1 System Risk Evaluation 4 1.2.2 Data in Risk Evaluation 6 1.2.3 Unit Interruption Cost 7 1.3 Outline of the Book 9 2 Outage Models of System Components 15 2.1 Introduction 15 2.2 Models of Independent Outages 16 2.2.1 Repairable Forced Failure 17 2.2.2 Aging Failure 18 2.2.3 Nonrepairable Chance Failure 24 2.2.4 Planned Outage 24 2.2.5 Semiforced Outage 27 2.2.6 Partial Failure Mode 28 2.2.7 Multiple Failure Mode 30 2.3 Models of Dependent Outages 31 2.3.1 Common-Cause Outage 31 2.3.2 Component-Group Outage 36 2.3.3 Station-Originated Outage 37 2.3.4 Cascading Outage 39 2.3.5 Environment-Dependent Failure 40 2.4 Conclusions 42 3 Parameter Estimation in Outage Models 45 3.1 Introduction 45 3.2 Point Estimation on Mean and Variance of Failure Data 46 3.2.1 Sample Mean 46 3.2.2 Sample Variance 48 3.3 Interval Estimation on Mean and Variance of Failure Data 49 3.3.1 General Concept of Confidence Interval 49 3.3.2 Confidence Interval of Mean 50 3.3.3 Confidence Interval of Variance 53 3.4 Estimating Failure Frequency of Individual Components 54 3.4.1 Point Estimation 54 3.4.2 Interval Estimation 55 3.5 Estimating Probability from a Binomial Distribution 56 3.6 Experimental Distribution of Failure Data and its Test 57 3.6.1 Experimental Distribution of Failure Data 58 3.6.2 Test of Experimental Distribution 59 3.7 Estimating Parameters in Aging Failure Models 60 3.7.1 Mean Life and its Standard Deviation in the Normal Model 61 3.7.2 Shape and Scale Parameters in the Weibull Model 63 3.7.3 Example 66 3.8 Conclusions 70 4 Elements of Risk Evaluation Methods 73 4.1 Introduction 73 4.2 Methods for Simple Systems 74 4.2.1 Probability Convolution 74 4.2.2 Series and Parallel Networks 75 4.2.3 Minimum Cutsets 78 4.2.4 Markov Equations 79 4.2.5 Frequency-Duration Approaches 81 4.3 Methods for Complex Systems 84 4.3.1 State Enumeration 84 4.3.2 Nonsequential Monte Carlo Simulation 87 4.3.3 Sequential Monte Carlo Simulation 89 4.4 Correlation Models in Risk Evaluation 91 4.4.1 Correlation Measures 92 4.4.2 Correlation Matrix Methods 93 4.4.3 Copula Functions 95 4.5 Conclusions 102 5 Risk Evaluation Techniques for Power Systems 105 5.1 Introduction 105 5.2 Techniques Used in Generation-Demand Systems 106 5.2.1 Convolution Technique 106 5.2.2 State Sampling Method 110 5.2.3 State Duration Sampling Method 112 5.3 Techniques Used in Radial Distribution Systems 114 5.3.1 Analytical Technique 114 5.3.2 State Duration Sampling Method 117 5.4 Techniques Used in Substation Configurations 118 5.4.1 Failure Modes and Modeling 119 5.4.2 Connectivity Identification 121 5.4.3 Stratified State Enumeration Method 123 5.4.4 State Duration Sampling Method 127 5.5 Techniques Used in Composite Generation and Transmission Systems 129 5.5.1 Basic Procedure 130 5.5.2 Component Failure Models 131 5.5.3 Load Curve Models 131 5.5.4 Contingency Analysis 133 5.5.5 Optimization Models for Load Curtailments 135 5.5.6 State Enumeration Method 138 5.5.7 State Sampling Method 139 5.6 Conclusions 141 6 Application of Risk Evaluation to Transmission Development Planning 143 6.1 Introduction 143 6.2 Concept of Probabilistic Planning 144 6.2.1 Basic Procedure 144 6.2.2 Cost Analysis 145 6.2.3 Present Value 146 6.3 Risk Evaluation Approach 146 6.3.1 Risk Evaluation Procedure 147 6.3.2 Risk Cost Model 147 6.4 Example 1: Selecting the Lowest-Cost Planning Alternative 149 6.4.1 System Description 149 6.4.2 Planning Alternatives 151 6.4.3 Risk Evaluation 152 6.4.4 Overall Economic Analysis 155 6.4.5 Summary 157 6.5 Example 2: Applying Different Planning Criteria 158 6.5.1 System and Planning Alternatives 158 6.5.2 Study Conditions and Data 159 6.5.3 Risk and Risk Cost Evaluation 161 6.5.4 Overall Economic Analysis 163 6.5.5 Summary 166 6.6 Conclusions 167 7 Application of Risk Evaluation to Transmission Operation Planning 169 7.1 Introduction 169 7.2 Concept of Risk Evaluation in Operation Planning 170 7.3 Risk Evaluation Method 173 7.4 Example 1: Determining the Lowest-Risk Operation Mode 175 7.4.1 System and Study Conditions 175 7.4.2 Assessing Impacts of Load Transfer 177 7.4.3 Comparing Different Reconfigurations 177 7.4.4 Selecting Operation Mode under the N−2 Condition 179 7.4.5 Summary 181 7.5 Example 2: A Simple Case by Hand Calculation 181 7.5.1 Basic Concept 181 7.5.2 Case Description 182 7.5.3 Study Conditions and Data 183 7.5.4 Risk Evaluation 185 7.5.5 Summary 188 7.6 Conclusions 188 8 Application of Risk Evaluation to Generation Source Planning 191 8.1 Introduction 191 8.2 Procedure of Reliability Planning 192 8.3 Simulation of Generation and Risk Costs 193 8.3.1 Simulation Approach 193 8.3.2 Minimization Cost Model 194 8.3.3 Expected Generation and Risk Costs 195 8.4 Example 1: Selecting Location and Size of Cogenerators 196 8.4.1 Basic Concept 196 8.4.2 System and Cogeneration Candidates 197 8.4.3 Risk Sensitivity Analysis 199 8.4.4 Maximum Benefit Analysis 201 8.4.5 Summary 205 8.5 Example 2: Making a Decision to Retire a Local Generation Plant 205 8.5.1 Case Description 206 8.5.2 Risk Evaluation 206 8.5.3 Total Cost Analysis 208 8.5.4 Summary 210 8.6 Conclusions 210 9 Application of Risk Evaluation to Selecting Substation Configurations 211 9.1 Introduction 211 9.2 Load Curtailment Model 212 9.3 Risk Evaluation Approach 215 9.3.1 Component Failure Models 215 9.3.2 Procedure of Risk Evaluation 215 9.3.3 Economic Analysis Method 216 9.4 Example 1: Selecting Substation Configuration 217 9.4.1 Two Substation Configurations 217 9.4.2 Risk Evaluation 218 9.4.3 Economic Analysis 222 9.4.4 Summary 223 9.5 Example 2: Evaluating Effects of Substation Configuration Changes 223 9.5.1 Simplified Model for Evaluating Substation Configurations 223 9.5.2 Problem Description 224 9.5.3 Risk Evaluation 227 9.5.4 Summary 228 9.6 Example 3: Selecting Transmission Line Arrangement Associated with Substations 229 9.6.1 Description of Two Options 229 9.6.2 Risk Evaluation and Economic Analysis 230 9.6.3 Summary 233 9.7 Conclusions 233 10 Application of Risk Evaluation to Renewable Energy Systems 235 10.1 Introduction 235 10.2 Risk Evaluation of Wind Turbine Power Converter System (WTPCS) 237 10.2.1 Basic Concepts 237 10.2.2 Power Losses and Temperatures of WTPCS Components 238 10.2.3 Risk Evaluation of WTPCS 240 10.2.4 Case Study 245 10.2.5 Summary 251 10.3 Risk Evaluation of Photovoltaic Power Systems 251 10.3.1 Two Basic Structures of Photovoltaic Power Systems 251 10.3.2 Risk Parameters of Photovoltaic Inverters 254 10.3.3 Risk Evaluation of Photovoltaic Power System 258 10.3.4 Case Study 263 10.3.5 Summary 270 10.4 Conclusions 272 11 Application of Risk Evaluation to Composite Systems with Renewable Sources 275 11.1 Introduction 275 11.2 Risk Assessment of a Composite System with Wind Farms and Solar Power Stations 276 11.2.1 Probability Models of Renewable Sources and Bus Load Curves 276 11.2.2 Multiple Correlations among Renewable Sources and Bus/Regional Loads 279 11.2.3 Risk Assessment Considering Multiple Correlations 282 11.2.4 Case Study 283 11.2.5 Summary 295 11.3 Determination of Transfer Capability Required by Wind Generation 296 11.3.1 System, Conditions, and Method 296 11.3.2 Wind Generation Model 298 11.3.3 Equivalence of Wind Power in Generation Systems 299 11.3.4 Transfer Capability Required by Wind Generation 303 11.3.5 Summary 309 11.4 Conclusions 310 12 Risk Evaluation of Wide Area Measurement and Control System 313 12.1 Introduction 313 12.2 Hierarchical Structure and Failure Analysis of WAMCS 314 12.2.1 Hierarchical Structure of WAMCS 314 12.2.2 Failure Analysis Technique for WAMCS 315 12.3 Risk Evaluation of Phasor Measurement Units 317 12.3.1 Markov State Models of PMU Modules 317 12.3.2 Equivalent Two-State Model of PMU 324 12.4 Risk Evaluation of Regional Communication Networks in WAMCS 325 12.4.1 Classification of Regional Communication Networks 325 12.4.2 Survival Mechanisms of Regional Networks 328 12.4.3 Risk Evaluation in Two Survival Mechanisms 329 12.4.4 Equivalent Two-State Model of a Regional Communication Network 334 12.5 Risk Evaluation of Backbone Network in WAMCS 335 12.5.1 Equivalent Risk Model of Backbone Communication Network 336 12.5.2 Risk Evaluation of Optic Fiber System 337 12.6 Numerical Results 343 12.6.1 Risk Indices of PMU 343 12.6.2 Risk Indices of Regional Communication Networks 345 12.6.3 Risk Indices of the Backbone Communication Network 347 12.6.4 Risk Indices of Overall WAMCS 348 12.7 Conclusions 349 13 Reliability-Centered Maintenance 351 13.1 Introduction 351 13.2 Basic Tasks in RCM 352 13.2.1 Comparison between Maintenance Alternatives 352 13.2.2 Lowest-Risk Maintenance Scheduling 353 13.2.3 Predictive Maintenance versus Corrective Maintenance 353 13.2.4 Ranking Importance of Components 354 13.3 Example 1: Transmission Maintenance Scheduling 355 13.3.1 Procedure of Transmission Maintenance Planning 355 13.3.2 Description of the System and Maintenance Outage 357 13.3.3 The Lowest-Risk Schedule of the Cable Replacement 358 13.3.4 Summary 359 13.4 Example 2: Workforce Planning in Maintenance 360 13.4.1 Problem Description 360 13.4.2 Procedure 361 13.4.3 Case Study and Results 362 13.4.4 Summary 363 13.5 Example 3: A Simple Case Performed by Hand Calculations 363 13.5.1 Case Description 363 13.5.2 Study Conditions and Data 365 13.5.3 EENS Evaluation 365 13.5.4 Summary 367 13.6 Conclusions 367 14 Probabilistic Spare-Equipment Analysis 369 14.1 Introduction 369 14.2 Spare-Equipment Analysis Based on Reliability Criteria 370 14.2.1 Unavailability of Components 370 14.2.2 Group Reliability and Spare-Equipment Analysis 372 14.3 Spare-Equipment Analysis Using the Probabilistic Cost Method 373 14.3.1 Failure Cost Model 373 14.3.2 Unit Failure Cost Estimation 374 14.3.3 Annual Investment Cost Model 375 14.3.4 Present Value Approach 375 14.3.5 Procedure of Spare-Equipment Analysis 376 14.4 Example 1: Determining Number and Timing of Spare Transformers 376 14.4.1 Transformer Group and Data 376 14.4.2 Spare-Transformer Analysis Based on Group Failure Probability 377 14.4.3 Spare-Transformer Plans Based on the Probabilistic Cost Model 378 14.4.4 Summary 381 14.5 Example 2: Determining Redundancy Level of 500 kV Reactors 381 14.5.1 Problem Description 381 14.5.2 Study Conditions and Data 383 14.5.3 Redundancy Analysis 385 14.5.4 Summary 387 14.6 Conclusions 387 15 Asset Management Based on Condition Monitoring and Risk Evaluation 389 15.1 Introduction 389 15.2 Maintenance Strategy of Overhead Lines 390 15.2.1 Risk Evaluation Using Condition Monitoring Data 391 15.2.2 Overhead Line Maintenance Strategy 397 15.2.3 Case Study 399 15.2.4 Summary 401 15.3 Replacement Strategy for Aged Transformers 402 15.3.1 Transformer Aging Failure Unavailability Using Condition Monitoring Data 403 15.3.2 Transformer Replacement Strategy 407 15.3.3 Case Study 410 15.3.4 Summary 413 15.4 Conclusions 414 16 Reliability-Based Transmission-Service Pricing 417 16.1 Introduction 417 16.2 Basic Concept 418 16.2.1 Incremental Reliability Value 419 16.2.2 Impacts of Customers on System Reliability 420 16.2.3 Reliability Component in Price Design 421 16.3 Calculation Methods 422 16.3.1 Unit Incremental Reliability Value 422 16.3.2 Generation Credit for Reliability Improvement 423 16.3.3 Load Charge for Reliability Degradation 423 16.3.4 Load Charge Rate Due to Generation Credit 424 16.4 Rate Design 424 16.4.1 Charge Rate for Wheeling Customers 424 16.4.2 Charge Rate for Native Customers 425 16.4.3 Credit to Generation Customers 425 16.5 Application Example 425 16.5.1 Calculation of the UIRV 427 16.5.2 Calculation of the GCRI 427 16.5.3 Calculation of the LCRD 427 16.5.4 Calculation of the LCRGC 428 16.5.5 Calculations of Charge Rates 428 16.6 Conclusions 430 17 Voltage Instability Risk Assessment and its Application to System Planning 431 17.1 Introduction 431 17.2 Method of Assessing Voltage Instability Risk 432 17.2.1 Maximum Loadability Model for System States 432 17.2.2 Models for Identifying Weak Branches and Buses 436 17.2.3 Determination of Contingency System States 443 17.2.4 Procedure of Calculating Voltage Instability Risk Indices 444 17.3 Tracing and Locating Voltage Instability Risk for Planning Alternatives 447 17.4 Case Studies 448 17.4.1 Results of the IEEE 14-Bus System 448 17.4.2 Results of the 171-Bus Utility System 453 17.5 Conclusions 456 18 Probabilistic Transient Stability Assessment 459 18.1 Introduction 459 18.2 Probabilistic Modeling and Simulation Methods 460 18.2.1 Selection of Pre-Fault System States 460 18.2.2 Fault Models 461 18.2.3 Monte Carlo Simulation of Fault Events 463 18.2.4 Transient Stability Simulation 464 18.3 Procedure 464 18.3.1 Procedure for the First Type of Study 465 18.3.2 Procedure for the Second Type of Study 465 18.4 Examples 465 18.4.1 System Description and Data 465 18.4.2 Transfer Limit Calculation in the Columbia River System 470 18.4.3 Generation Rejection Requirement in the Peace River System 472 18.4.4 Summary 475 18.5 Conclusions 475 Appendix A Basic Probability Concepts 477 A.1 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 Distribution 479 A.3.2 Normal Distribution 479 A.3.3 Log-Normal Distribution 481 A.3.4 Weibull 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 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.1 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.1 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.1 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

About the Author :
DR. WENYUAN LI, PhD, is recognized as one of the leading authorities on risk assessment of power systems and has been active in power system risk and reliability evaluation for more than twenty-five years. He is a full professor with Chongqing University, China, and a principal engineer at BC Hydro, Canada. He is a fellow of the Canadian Academy of Engineering, the Engineering Institute of Canada, and the IEEE, and received ten international awards due to his significant contributions in the power system risk assessment field.