About the Companion Website xiii
1 Introduction 1
1.1 Importance of Modeling and Understanding Cascading Failures 1
1.1.1 Cascading Failures 1
1.1.2 Challenges in Modeling and Understanding Cascading Failures 4
1.2 Importance of Controlled System Separation 6
1.2.1 Mitigation of Cascading Failures 6
1.2.2 Uncontrolled and Controlled System Separations 7
1.3 Constructing Restoration Strategies 9
1.3.1 Importance of System Restoration 9
1.3.2 Classification of System Restoration Strategies 10
1.3.3 Challenges of System Restoration 13
1.4 Overview of the Book 15
References 18
2 Modeling of Cascading Failures 23
2.1 General Cascading Failure Models 23
2.1.1 Bakâ"Tangâ"Wiesenfeld Sandpile Model 23
2.1.2 FailureâTolerance Sandpile Model 24
2.1.3 Motterâ"Lai Model 30
2.1.4 Influence Model 30
2.1.5 BinaryâDecision Model 33
2.1.6 Coupled Map Lattice Model 34
2.1.7 CASCADE Model 35
2.1.8 Interdependent Failure Model 37
2.2 Power System Cascading Failure Models 39
2.2.1 Hidden Failure Model 39
2.2.2 Manchester Model 40
2.2.3 OPA Model 42
2.2.4 Improved OPA Model 46
2.2.5 OPA Model with Slow Process 49
2.2.6 AC OPA Model 58
2.2.7 Cascading Failure Models Considering Dynamics and Detailed Protections 62
References 64
3 Understanding Cascading Failures 69
3.1 Selfâ Organized Criticality 70
3.1.1 SOC Theory 70
3.1.2 Evidence of SOC in Blackout Data 71
3.2 Branching Processes 72
3.2.1 Definition of the Galtonâ"Watson Branching Process 74
3.2.2 Estimation of Mean of the Offspring Distribution 74
3.2.3 Estimation of Variance of the Offspring Distribution 75
3.2.4 Processing and Discretization of Continuous Data 78
3.2.5 Estimation of Distribution of Total Outages 81
3.2.6 Statistical Insight of Branching Process Parameters 81
3.2.7 Branching Processes Applied to Line Outage Data 82
3.2.8 Branching Processes Applied to Load Shed Data 84
3.2.9 CrossâValidation for Branching Processes 85
3.2.10 Efficiency Improvement by Branching Processes 85
3.3 Multitype Branching Processes 87
3.3.1 Estimation of Multitype Branching Process Parameters 88
3.3.2 Estimation of Joint Probability Distribution of Total Outages 90
3.3.3 An Example for a TwoâType Branching Process 91
3.3.4 Validation of Estimated Joint Distribution 92
3.3.5 Number of Cascades Needed for Multitype Branching Processes 94
3.3.6 Estimated Parameters of Branching Processes 96
3.3.7 Estimated Joint Distribution of Total Outages 98
3.3.8 CrossâValidation for Multitype Branching Processes 100
3.3.9 Predicting Joint Distribution from One Type of Outage 102
3.3.10 Estimating Failure Propagation of Three Types of Outages 104
3.4 Failure Interaction Analysis 105
3.4.1 Estimation of Interactions between Component Failures 106
3.4.2 Identification of Key Links and Key Components 108
3.4.3 Interaction Model 111
3.4.4 Validation of Interaction Model 113
3.4.5 Number of Cascades Needed for Failure Interaction Analysis 115
3.4.6 Estimated Interaction Matrix and Interaction Network 119
3.4.7 Identified Key Links and Key Components 121
3.4.8 Interaction Model Validation 125
3.4.9 Cascading Failure Mitigation 129
3.4.10 Efficiency Improvement by Interaction Model 134
References 137
4 Strategies for Controlled System Separation 141
4.1 Questions to Answer 141
4.2 Literature Review 142
4.3 Constraints on Separation Points 144
4.4 Graph Models of a Power Network 148
4.4.1 Undirected NodeâWeighted Graph 149
4.4.2 Directed EdgeâWeighted Graph 152
4.5 Generator Grouping 153
4.5.1 Slow Coherency Analysis 154
4.5.2 Elementary Coherent Groups 158
4.6 Finding Separation Points 160
4.6.1 Formulations of the Problem 160
4.6.2 Computational Complexity 164
4.6.3 Network Reduction 167
4.6.4 Network Decomposition for Parallel Processing 173
4.6.5 Application of the Ordered Binary Decision Diagram 175
4.6.6 Checking the Transmission Capacity and Small Disruption Constraints 185
4.6.7 Checking All Constraints in Three Steps 190
References 192
5 Online Decision Support for Controlled System Separation 197
5.1 Online Decision on the Separation Strategy 197
5.1.1 Spectral Analysis-Based Method 198
5.1.2 FrequencyâAmplitude Characteristics of Electromechanical Oscillation 199
5.1.3 PhaseâLocked Loop-Based Method 204
5.1.4 Timing of Controlled Separation 210
5.2 WAMSâ Based Unified Framework for Controlled System Separation 212
5.2.1 WAMSâBased ThreeâStage CSS Scheme 212
5.2.2 Offline Analysis Stage 214
5.2.3 Online Monitoring Stage 216
5.2.4 RealâTime Control Stage 221
References 223
6 Constraints of System Restoration 225
6.1 Physical Constraints During Restoration 225
6.1.1 Generating Unit StartâUp 225
6.1.2 System Sectionalizing and Reconfiguration 230
6.1.3 Load Restoration 233
6.2 Electromagnetic Transients During System Restoration 235
6.2.1 Generator SelfâExcitation 237
6.2.2 Switching Overvoltage 237
6.2.3 Resonant Overvoltage in the Case of Energizing NoâLoad Transformer 242
6.2.4 Impact of Magnetizing Inrush Current on Transformer 245
6.2.5 Voltage and Frequency Analysis in Picking up Load 247
References 251
7 Restoration Methodology and Implementation Algorithms 255
7.1 Algorithms for Generating Unit StartâUp 255
7.1.1 A General Bilevel Framework 255
7.1.2 Algorithms for the Primary Problem 260
7.1.3 Algorithms for the Second Problem 265
7.2 Algorithms for Load Restoration 269
7.2.1 Estimate Operational Region Bound 271
7.2.2 Formulate MINLR Model to Maximize Load Pickup 272
7.2.3 BranchâandâCut Solver: Design and Justification 275
7.2.4 Selection of Branching Methods 278
7.3 Case Studies 278
7.3.1 Illustrative Example for Restoring Generating Units 278
7.3.2 Optimal Load Restoration Strategies for RTS 24âBus System 283
7.3.3 Optimal Load Restoration Strategies for IEEE 118âBus System 287
References 291
8 Renewable and Energy Storage in System Restoration 295
8.1 Planning of Renewable Generators in System Restoration 295
8.1.1 Renewables for System Restoration 295
8.1.2 The Offline Restoration Tool Using Renewable Energy Resources 296
8.1.3 System Restoration with Renewablesâ Participation 298
8.2 Operation and Control of Renewable Generators in System Restoration 305
8.2.1 Prerequisites of Type 3 WTs for System Restoration 307
8.2.2 Problem Setup of Type 3 WTs for System Restoration 308
8.2.3 BlackâStarting Control and Sequence of Type 3 WTs 314
8.2.4 Autonomous Frequency Mechanism of a Type 3 WT-Based StandâAlone System 317
8.2.5 Simulation Study 320
8.3 Energy Storage in System Restoration 323
8.3.1 PumpedâStorage Hydro Units in Restoration 323
8.3.2 Batteries for System Restoration 332
8.3.3 Electric Vehicles in System Restoration 340
References 351
9 Emerging Technologies in System Restoration 357
9.1 Applications of FACTS and HVDC 357
9.1.1 LCCâHVDC Technology for System Restoration 357
9.1.2 VSCâHVDC Technology for System Restoration 363
9.1.3 FACTS Technology for System Restoration 370
9.2 Applications of PMUs 376
9.2.1 Review of PMU 376
9.2.2 System Restoration with PMU Measurements 378
9.3 Microgrid in System Restoration 385
9.3.1 MicrogridâBased Restoration 385
9.3.2 Demonstration and Practice 388
References 393
10 Black-Start Capability Assessment and Optimization 399
10.1 Background of Black Start 399
10.1.1 Definition of Black Start 399
10.1.2 Constraints During BS 400
10.1.3 BS Service Procurement 401
10.1.4 Power System Restoration Procedure 403
10.2 BS Capability Assessment 404
10.2.1 Installation Criteria of New BS Generators 404
10.2.2 Optimal Installation Strategy of BS Capability 407
10.2.3 Examples 408
10.3 Optimal BS Capability 411
10.3.1 Problem Formulation 411
10.3.2 Solution Algorithm 418
10.3.3 Examples 421
References 431
Index 433
