Risk Assessment of Power Systems

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.

• Preface xixPreface to the First Edition xxi1 Introduction 11.1 Risk in Power Systems 11.2 Basic Concepts of Power System Risk Assessment 41.2.1 System Risk Evaluation 41.2.2 Data in Risk Evaluation 61.2.3 Unit Interruption Cost 71.3 Outline of the Book 92 Outage Models of System Components 152.1 Introduction 152.2 Models of Independent Outages 162.2.1 Repairable Forced Failure 172.2.2 Aging Failure 182.2.3 Nonrepairable Chance Failure 242.2.4 Planned Outage 242.2.5 Semiforced Outage 272.2.6 Partial Failure Mode 282.2.7 Multiple Failure Mode 302.3 Models of Dependent Outages 312.3.1 Common-Cause Outage 312.3.2 Component-Group Outage 362.3.3 Station-Originated Outage 372.3.4 Cascading Outage 392.3.5 Environment-Dependent Failure 402.4 Conclusions 423 Parameter Estimation in Outage Models 453.1 Introduction 453.2 Point Estimation on Mean and Variance of Failure Data 463.2.1 Sample Mean 463.2.2 Sample Variance 483.3 Interval Estimation on Mean and Variance of Failure Data 493.3.1 General Concept of Confidence Interval 493.3.2 Confidence Interval of Mean 503.3.3 Confidence Interval of Variance 533.4 Estimating Failure Frequency of Individual Components 543.4.1 Point Estimation 543.4.2 Interval Estimation 553.5 Estimating Probability from a Binomial Distribution 563.6 Experimental Distribution of Failure Data and its Test 573.6.1 Experimental Distribution of Failure Data 583.6.2 Test of Experimental Distribution 593.7 Estimating Parameters in Aging Failure Models 603.7.1 Mean Life and its Standard Deviation in the Normal Model 613.7.2 Shape and Scale Parameters in the Weibull Model 633.7.3 Example 663.8 Conclusions 704 Elements of Risk Evaluation Methods 734.1 Introduction 734.2 Methods for Simple Systems 744.2.1 Probability Convolution 744.2.2 Series and Parallel Networks 754.2.3 Minimum Cutsets 784.2.4 Markov Equations 794.2.5 Frequency-Duration Approaches 814.3 Methods for Complex Systems 844.3.1 State Enumeration 844.3.2 Nonsequential Monte Carlo Simulation 874.3.3 Sequential Monte Carlo Simulation 894.4 Correlation Models in Risk Evaluation 914.4.1 Correlation Measures 924.4.2 Correlation Matrix Methods 934.4.3 Copula Functions 954.5 Conclusions 1025 Risk Evaluation Techniques for Power Systems 1055.1 Introduction 1055.2 Techniques Used in Generation-Demand Systems 1065.2.1 Convolution Technique 1065.2.2 State Sampling Method 1105.2.3 State Duration Sampling Method 1125.3 Techniques Used in Radial Distribution Systems 1145.3.1 Analytical Technique 1145.3.2 State Duration Sampling Method 1175.4 Techniques Used in Substation Configurations 1185.4.1 Failure Modes and Modeling 1195.4.2 Connectivity Identification 1215.4.3 Stratified State Enumeration Method 1235.4.4 State Duration Sampling Method 1275.5 Techniques Used in Composite Generation and Transmission Systems 1295.5.1 Basic Procedure 1305.5.2 Component Failure Models 1315.5.3 Load Curve Models 1315.5.4 Contingency Analysis 1335.5.5 Optimization Models for Load Curtailments 1355.5.6 State Enumeration Method 1385.5.7 State Sampling Method 1395.6 Conclusions 1416 Application of Risk Evaluation to Transmission Development Planning 1436.1 Introduction 1436.2 Concept of Probabilistic Planning 1446.2.1 Basic Procedure 1446.2.2 Cost Analysis 1456.2.3 Present Value 1466.3 Risk Evaluation Approach 1466.3.1 Risk Evaluation Procedure 1476.3.2 Risk Cost Model 1476.4 Example 1: Selecting the Lowest-Cost Planning Alternative 1496.4.1 System Description 1496.4.2 Planning Alternatives 1516.4.3 Risk Evaluation 1526.4.4 Overall Economic Analysis 1556.4.5 Summary 1576.5 Example 2: Applying Different Planning Criteria 1586.5.1 System and Planning Alternatives 1586.5.2 Study Conditions and Data 1596.5.3 Risk and Risk Cost Evaluation 1616.5.4 Overall Economic Analysis 1636.5.5 Summary 1666.6 Conclusions 1677 Application of Risk Evaluation to Transmission Operation Planning 1697.1 Introduction 1697.2 Concept of Risk Evaluation in Operation Planning 1707.3 Risk Evaluation Method 1737.4 Example 1: Determining the Lowest-Risk Operation Mode 1757.4.1 System and Study Conditions 1757.4.2 Assessing Impacts of Load Transfer 1777.4.3 Comparing Different Reconfigurations 1777.4.4 Selecting Operation Mode under the N−2 Condition 1797.4.5 Summary 1817.5 Example 2: A Simple Case by Hand Calculation 1817.5.1 Basic Concept 1817.5.2 Case Description 1827.5.3 Study Conditions and Data 1837.5.4 Risk Evaluation 1857.5.5 Summary 1887.6 Conclusions 1888 Application of Risk Evaluation to Generation Source Planning 1918.1 Introduction 1918.2 Procedure of Reliability Planning 1928.3 Simulation of Generation and Risk Costs 1938.3.1 Simulation Approach 1938.3.2 Minimization Cost Model 1948.3.3 Expected Generation and Risk Costs 1958.4 Example 1: Selecting Location and Size of Cogenerators 1968.4.1 Basic Concept 1968.4.2 System and Cogeneration Candidates 1978.4.3 Risk Sensitivity Analysis 1998.4.4 Maximum Benefit Analysis 2018.4.5 Summary 2058.5 Example 2: Making a Decision to Retire a Local Generation Plant 2058.5.1 Case Description 2068.5.2 Risk Evaluation 2068.5.3 Total Cost Analysis 2088.5.4 Summary 2108.6 Conclusions 2109 Application of Risk Evaluation to Selecting Substation Configurations 2119.1 Introduction 2119.2 Load Curtailment Model 2129.3 Risk Evaluation Approach 2159.3.1 Component Failure Models 2159.3.2 Procedure of Risk Evaluation 2159.3.3 Economic Analysis Method 2169.4 Example 1: Selecting Substation Configuration 2179.4.1 Two Substation Configurations 2179.4.2 Risk Evaluation 2189.4.3 Economic Analysis 2229.4.4 Summary 2239.5 Example 2: Evaluating Effects of Substation Configuration Changes 2239.5.1 Simplified Model for Evaluating Substation Configurations 2239.5.2 Problem Description 2249.5.3 Risk Evaluation 2279.5.4 Summary 2289.6 Example 3: Selecting Transmission Line Arrangement Associated with Substations 2299.6.1 Description of Two Options 2299.6.2 Risk Evaluation and Economic Analysis 2309.6.3 Summary 2339.7 Conclusions 23310 Application of Risk Evaluation to Renewable Energy Systems 235 10.1 Introduction 23510.2 Risk Evaluation of Wind Turbine Power Converter System (WTPCS) 23710.2.1 Basic Concepts 23710.2.2 Power Losses and Temperatures of WTPCS Components 23810.2.3 Risk Evaluation of WTPCS 24010.2.4 Case Study 24510.2.5 Summary 25110.3 Risk Evaluation of Photovoltaic Power Systems 25110.3.1 Two Basic Structures of Photovoltaic Power Systems 25110.3.2 Risk Parameters of Photovoltaic Inverters 25410.3.3 Risk Evaluation of Photovoltaic Power System 25810.3.4 Case Study 26310.3.5 Summary 27010.4 Conclusions 27211 Application of Risk Evaluation to Composite Systems with Renewable Sources 27511.1 Introduction 27511.2 Risk Assessment of a Composite System with Wind Farms and Solar Power Stations 27611.2.1 Probability Models of Renewable Sources and Bus Load Curves 27611.2.2 Multiple Correlations among Renewable Sources and Bus/Regional Loads 27911.2.3 Risk Assessment Considering Multiple Correlations 28211.2.4 Case Study 28311.2.5 Summary 29511.3 Determination of Transfer Capability Required by Wind Generation 29611.3.1 System, Conditions, and Method 29611.3.2 Wind Generation Model 29811.3.3 Equivalence of Wind Power in Generation Systems 29911.3.4 Transfer Capability Required by Wind Generation 30311.3.5 Summary 30911.4 Conclusions 31012 Risk Evaluation of Wide Area Measurement and Control System 31312.1 Introduction 31312.2 Hierarchical Structure and Failure Analysis of WAMCS 31412.2.1 Hierarchical Structure of WAMCS 31412.2.2 Failure Analysis Technique for WAMCS 31512.3 Risk Evaluation of Phasor Measurement Units 31712.3.1 Markov State Models of PMU Modules 31712.3.2 Equivalent Two-State Model of PMU 32412.4 Risk Evaluation of Regional Communication Networks in WAMCS 32512.4.1 Classification of Regional Communication Networks 32512.4.2 Survival Mechanisms of Regional Networks 32812.4.3 Risk Evaluation in Two Survival Mechanisms 32912.4.4 Equivalent Two-State Model of a Regional Communication Network 33412.5 Risk Evaluation of Backbone Network in WAMCS 33512.5.1 Equivalent Risk Model of Backbone Communication Network 33612.5.2 Risk Evaluation of Optic Fiber System 33712.6 Numerical Results 34312.6.1 Risk Indices of PMU 34312.6.2 Risk Indices of Regional Communication Networks 34512.6.3 Risk Indices of the Backbone Communication Network 34712.6.4 Risk Indices of Overall WAMCS 34812.7 Conclusions 34913 Reliability-Centered Maintenance 35113.1 Introduction 35113.2 Basic Tasks in RCM 35213.2.1 Comparison between Maintenance Alternatives 35213.2.2 Lowest-Risk Maintenance Scheduling 35313.2.3 Predictive Maintenance versus Corrective Maintenance 35313.2.4 Ranking Importance of Components 35413.3 Example 1: Transmission Maintenance Scheduling 35513.3.1 Procedure of Transmission Maintenance Planning 35513.3.2 Description of the System and Maintenance Outage 35713.3.3 The Lowest-Risk Schedule of the Cable Replacement 35813.3.4 Summary 35913.4 Example 2: Workforce Planning in Maintenance 36013.4.1 Problem Description 36013.4.2 Procedure 36113.4.3 Case Study and Results 36213.4.4 Summary 36313.5 Example 3: A Simple Case Performed by Hand Calculations 36313.5.1 Case Description 36313.5.2 Study Conditions and Data 36513.5.3 EENS Evaluation 36513.5.4 Summary 36713.6 Conclusions 36714 Probabilistic Spare-Equipment Analysis 36914.1 Introduction 36914.2 Spare-Equipment Analysis Based on Reliability Criteria 37014.2.1 Unavailability of Components 37014.2.2 Group Reliability and Spare-Equipment Analysis 37214.3 Spare-Equipment Analysis Using the Probabilistic Cost Method 37314.3.1 Failure Cost Model 37314.3.2 Unit Failure Cost Estimation 37414.3.3 Annual Investment Cost Model 37514.3.4 Present Value Approach 37514.3.5 Procedure of Spare-Equipment Analysis 37614.4 Example 1: Determining Number and Timing of Spare Transformers 37614.4.1 Transformer Group and Data 37614.4.2 Spare-Transformer Analysis Based on Group Failure Probability 37714.4.3 Spare-Transformer Plans Based on the Probabilistic Cost Model 37814.4.4 Summary 38114.5 Example 2: Determining Redundancy Level of 500 kV Reactors 38114.5.1 Problem Description 38114.5.2 Study Conditions and Data 38314.5.3 Redundancy Analysis 38514.5.4 Summary 38714.6 Conclusions 38715 Asset Management Based on Condition Monitoring and Risk Evaluation 38915.1 Introduction 38915.2 Maintenance Strategy of Overhead Lines 39015.2.1 Risk Evaluation Using Condition Monitoring Data 39115.2.2 Overhead Line Maintenance Strategy 39715.2.3 Case Study 39915.2.4 Summary 40115.3 Replacement Strategy for Aged Transformers 40215.3.1 Transformer Aging Failure Unavailability Using Condition Monitoring Data 40315.3.2 Transformer Replacement Strategy 40715.3.3 Case Study 41015.3.4 Summary 41315.4 Conclusions 41416 Reliability-Based Transmission-Service Pricing 41716.1 Introduction 41716.2 Basic Concept 41816.2.1 Incremental Reliability Value 41916.2.2 Impacts of Customers on System Reliability 42016.2.3 Reliability Component in Price Design 42116.3 Calculation Methods 42216.3.1 Unit Incremental Reliability Value 42216.3.2 Generation Credit for Reliability Improvement 42316.3.3 Load Charge for Reliability Degradation 42316.3.4 Load Charge Rate Due to Generation Credit 42416.4 Rate Design 42416.4.1 Charge Rate for Wheeling Customers 42416.4.2 Charge Rate for Native Customers 42516.4.3 Credit to Generation Customers 42516.5 Application Example 42516.5.1 Calculation of the UIRV 42716.5.2 Calculation of the GCRI 42716.5.3 Calculation of the LCRD 42716.5.4 Calculation of the LCRGC 42816.5.5 Calculations of Charge Rates 42816.6 Conclusions 43017 Voltage Instability Risk Assessment and its Application to System Planning 43117.1 Introduction 43117.2 Method of Assessing Voltage Instability Risk 43217.2.1 Maximum Loadability Model for System States 43217.2.2 Models for Identifying Weak Branches and Buses 43617.2.3 Determination of Contingency System States 44317.2.4 Procedure of Calculating Voltage Instability Risk Indices 44417.3 Tracing and Locating Voltage Instability Risk for Planning Alternatives 44717.4 Case Studies 44817.4.1 Results of the IEEE 14-Bus System 44817.4.2 Results of the 171-Bus Utility System 45317.5 Conclusions 45618 Probabilistic Transient Stability Assessment 45918.1 Introduction 45918.2 Probabilistic Modeling and Simulation Methods 46018.2.1 Selection of Pre-Fault System States 46018.2.2 Fault Models 46118.2.3 Monte Carlo Simulation of Fault Events 46318.2.4 Transient Stability Simulation 46418.3 Procedure 46418.3.1 Procedure for the First Type of Study 46518.3.2 Procedure for the Second Type of Study 46518.4 Examples 46518.4.1 System Description and Data 46518.4.2 Transfer Limit Calculation in the Columbia River System 47018.4.3 Generation Rejection Requirement in the Peace River System 47218.4.4 Summary 47518.5 Conclusions 475Appendix A Basic Probability Concepts 477A.1 Probability Calculation Rules 477A.1.1 Intersection 477A.1.2 Union 477A.1.3 Full Conditional Probability 478A.2 Random Variable and its Distribution 478A.3 Important Distributions in Risk Evaluation 479A.3.1 Exponential Distribution 479A.3.2 Normal Distribution 479A.3.3 Log-Normal Distribution 481A.3.4 Weibull Distribution 481A.3.5 Gamma Distribution 482A.3.6 Beta Distribution 483A.4 Numerical Characteristics 483A.4.1 Mathematical Expectation 483A.4.2 Variance and Standard Deviation 484A.4.3 Covariance and Correlation Coefficients 484A.5 Nonparametric Kernel Density Estimator 485A.5.1 Basic Concept 485A.5.2 Determination of the Bandwidth 486Appendix B Elements of Monte Carlo Simulation 489B.1 General Concept 489B.2 Random Number Generators 490B.2.1 Multiplicative Congruent Generator 490B.2.2 Mixed Congruent Generator 491B.3 Inverse Transform Method of Generating Random Variates 491B.4 Important Random Variates in Risk Evaluation 492B.4.1 Exponential Distribution Random Variate 492B.4.2 Normal Distribution Random Variate 493B.4.3 Log-Normal Distribution Random Variate 494B.4.4 Weibull Distribution Random Variate 494B.4.5 Gamma Distribution Random Variate 495B.4.6 Beta Distribution Random Variate 495Appendix C Power Flow Models 497C.1 AC Power Flow Models 497C.1.1 Power Flow Equations 497C.1.2 Newton–Raphson Method 497C.1.3 Fast Decoupled Method 498C.2 DC Power Flow Models 499C.2.1 Basic Equation 499C.2.2 Line Flow Equation 500Appendix D Optimization Algorithms 503D.1 Simplex Methods for Linear Programming 503D.1.1 Primal Simplex Method 503D.1.2 Dual Simplex Method 505D.2 Interior Point Method for Nonlinear Programming 506D.2.1 Optimality and Feasibility Conditions 506D.2.2 Procedure of the Algorithm 508Appendix E Three Probability Distribution Tables 511References 515Further Reading 523Index 525