Risk Assessment of Power Systems: Models, Methods, and Applications

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.

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 Confi dence Interval / 49 3.3.2 Confi dence Interval of Mean / 50 3.3.3 Confi dence 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 Confi gurations / 118 5.4.1 Failure Modes and Modeling / 119 5.4.2 Connectivity Identifi cation / 121 5.4.3 Stratifi ed 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 Reconfi gurations / 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 Benefi t 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 Confi guration / 217 9.4.1 Two Substation Confi gurations / 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 Confi guration Changes / 223 9.5.1 Simplifi ed Model for Evaluating Substation Confi gurations / 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 Classifi cation 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 Coeffi cients / 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

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.