Preface xiii
Acknowledgments xv
Figures xvii
Tables xxi
Part I Concepts and Methods in System Reliability 1
1 Introduction to Reliability 3
1.1 Introduction 3
1.2 Quantitative Reliability 4
1.3 Basic Approaches for Considering Reliability in Decision-Making 6
1.4 Objective and Scope of This Book 8
1.5 Organization of This Book 9
2 Review of Probability Theory 11
2.1 Introduction 11
2.2 State Space and Event 11
2.3 Probability Measure and Related Rules 16
2.4 Random Variables 25
2.5 Jointly Distributed Random Variables 31
2.6 Expectation, Variance, Covariance and Correlation 32
2.7 Moment Generating Function 36
2.8 Functions of Random Variables 39
Exercises 51
3 Review of Stochastic Process 53
3.1 Introduction 53
3.2 Discrete-Time Markov Process 57
3.3 Continuous-Time Markov Process 72
Exercises 80
4 Frequency-Based Approach to Stochastic Process 81
4.1 Introduction 81
4.2 Concept of Transition Rate 82
4.3 Concept of Frequency 83
4.4 Concept of Frequency Balance 91
4.5 Equivalent Transition Rate 100
4.6 Coherence 102
4.7 Conditional Frequency 104
4.8 Time-Specific Frequency 109
4.9 Probability to Frequency Conversion Rules 110
Exercises 115
5 Analytical Methods in Reliability Analysis 117
5.1 Introduction 117
5.2 State Space Approach 117
5.3 Network Reduction Method 139
5.4 Conditional Probability Method 147
5.5 Cut-Set and Tie-Set Methods 152
Exercises 164
6 Monte Carlo Simulation 165
6.1 Introduction 165
6.2 Random Number Generation 166
6.3 Classification of Monte Carlo Simulation Methods 167
6.4 Estimation and Convergence in Sampling 174
6.5 Variance Reduction Techniques 178
Exercises 182
Part II Methods of Power System Reliability Modeling and Analysis 185
7 Introduction to Power System Reliability 187
7.1 Introduction 187
7.2 Scope of Power System Reliability Studies 187
7.3 Power System Reliability Indices 188
7.4 Considerations in Power System Reliability Evaluation 190
8 Generation Adequacy Evaluation Using Discrete Convolution 193
8.1 Introduction 193
8.2 Generation Model 193
8.3 Load Model 205
8.4 Generation Reserve Model 208
8.5 Determination of Reliability Indices 210
8.6 Conclusion 212
Exercises 213
9 Reliability Analysis of Multinode Power Systems 215
9.1 Introduction 215
9.2 Scope and Modeling of Multinode Systems 215
9.3 System Modeling 216
9.4 Power Flow Models and Operating Policies 222
10 Reliability Evaluation of Multi-Area Power Systems 227
10.1 Introduction 227
10.2 Overview of Methods for Multi-Area System Studies 227
10.3 The Method of State Space Decomposition 229
10.4 Conclusion 245
Exercises 245
11 Reliability Evaluation of Composite Power Systems 247
11.1 Introduction 247
11.2 Analytical Methods 247
11.3 Monte Carlo Simulation 250
11.4 Sequential Simulation 250
11.5 Nonsequential Simulation 254
11.6 Testing of States 262
11.7 Acceleration of Convergence 263
11.8 State Space Pruning: Concept and Method 263
11.9 Intelligent Search Techniques 268
11.10 Conclusion 272
12 Power System Reliability Considerations in Energy Planning 273
12.1 Introduction 273
12.2 Problem Formulation 275
12.3 Sample Average Approximation (SAA) 279
12.4 Computational Results 282
12.5 Conclusion and Discussion 288
13 Modeling of Variable Energy Resources 291
13.1 Introduction 291
13.2 Characteristics of Variable Energy Resources 292
13.3 Variable Resource Modeling Approaches 293
13.4 Integrating Renewables at the Composite System Level 301
14 Concluding Reflections 305
Bibliography 309
Index 321
