KAI SUN is an Associate Professor with the Department of Electrical Engineering and Computer Science at the University of Tennessee, USA. YUNHE HOU is an Associate Professor with the Department of Electrical and Electronic Engineering, University of Hong Kong. WEI SUN is an Assistant Professor in the Department of Electrical and Computer Engineering of the University of Central Florida, USA. JUNJIAN QI is an Assistant Professor in the Department of Electrical and Computer Engineering of the University of Central Florida, USA.

• About the Companion Website xiii1 Introduction 11.1 Importance of Modeling and Understanding Cascading Failures 11.1.1 Cascading Failures 11.1.2 Challenges in Modeling and Understanding Cascading Failures 41.2 Importance of Controlled System Separation 61.2.1 Mitigation of Cascading Failures 61.2.2 Uncontrolled and Controlled System Separations 71.3 Constructing Restoration Strategies 91.3.1 Importance of System Restoration 91.3.2 Classification of System Restoration Strategies 101.3.3 Challenges of System Restoration 131.4 Overview of the Book 15References 182 Modeling of Cascading Failures 232.1 General Cascading Failure Models 232.1.1 Bak–Tang–Wiesenfeld Sandpile Model 232.1.2 Failure‐Tolerance Sandpile Model 242.1.3 Motter–Lai Model 302.1.4 Influence Model 302.1.5 Binary‐Decision Model 332.1.6 Coupled Map Lattice Model 342.1.7 CASCADE Model 352.1.8 Interdependent Failure Model 372.2 Power System Cascading Failure Models 392.2.1 Hidden Failure Model 392.2.2 Manchester Model 402.2.3 OPA Model 422.2.4 Improved OPA Model 462.2.5 OPA Model with Slow Process 492.2.6 AC OPA Model 582.2.7 Cascading Failure Models Considering Dynamics and Detailed Protections 62References 643 Understanding Cascading Failures 693.1 Self‐ Organized Criticality 703.1.1 SOC Theory 703.1.2 Evidence of SOC in Blackout Data 713.2 Branching Processes 723.2.1 Definition of the Galton–Watson Branching Process 743.2.2 Estimation of Mean of the Offspring Distribution 743.2.3 Estimation of Variance of the Offspring Distribution 753.2.4 Processing and Discretization of Continuous Data 783.2.5 Estimation of Distribution of Total Outages 813.2.6 Statistical Insight of Branching Process Parameters 813.2.7 Branching Processes Applied to Line Outage Data 823.2.8 Branching Processes Applied to Load Shed Data 843.2.9 Cross‐Validation for Branching Processes 853.2.10 Efficiency Improvement by Branching Processes 853.3 Multitype Branching Processes 873.3.1 Estimation of Multitype Branching Process Parameters 883.3.2 Estimation of Joint Probability Distribution of Total Outages 903.3.3 An Example for a Two‐Type Branching Process 913.3.4 Validation of Estimated Joint Distribution 923.3.5 Number of Cascades Needed for Multitype Branching Processes 943.3.6 Estimated Parameters of Branching Processes 963.3.7 Estimated Joint Distribution of Total Outages 983.3.8 Cross‐Validation for Multitype Branching Processes 1003.3.9 Predicting Joint Distribution from One Type of Outage 1023.3.10 Estimating Failure Propagation of Three Types of Outages 1043.4 Failure Interaction Analysis 1053.4.1 Estimation of Interactions between Component Failures 1063.4.2 Identification of Key Links and Key Components 1083.4.3 Interaction Model 1113.4.4 Validation of Interaction Model 1133.4.5 Number of Cascades Needed for Failure Interaction Analysis 1153.4.6 Estimated Interaction Matrix and Interaction Network 1193.4.7 Identified Key Links and Key Components 1213.4.8 Interaction Model Validation 1253.4.9 Cascading Failure Mitigation 1293.4.10 Efficiency Improvement by Interaction Model 134References 1374 Strategies for Controlled System Separation 1414.1 Questions to Answer 1414.2 Literature Review 1424.3 Constraints on Separation Points 1444.4 Graph Models of a Power Network 1484.4.1 Undirected Node‐Weighted Graph 1494.4.2 Directed Edge‐Weighted Graph 1524.5 Generator Grouping 1534.5.1 Slow Coherency Analysis 1544.5.2 Elementary Coherent Groups 1584.6 Finding Separation Points 1604.6.1 Formulations of the Problem 1604.6.2 Computational Complexity 1644.6.3 Network Reduction 1674.6.4 Network Decomposition for Parallel Processing 1734.6.5 Application of the Ordered Binary Decision Diagram 1754.6.6 Checking the Transmission Capacity and Small Disruption Constraints 1854.6.7 Checking All Constraints in Three Steps 190References 1925 Online Decision Support for Controlled System Separation 1975.1 Online Decision on the Separation Strategy 1975.1.1 Spectral Analysis-Based Method 1985.1.2 Frequency‐Amplitude Characteristics of Electromechanical Oscillation 1995.1.3 Phase‐Locked Loop-Based Method 2045.1.4 Timing of Controlled Separation 2105.2 WAMS‐ Based Unified Framework for Controlled System Separation 2125.2.1 WAMS‐Based Three‐Stage CSS Scheme 2125.2.2 Offline Analysis Stage 2145.2.3 Online Monitoring Stage 2165.2.4 Real‐Time Control Stage 221References 2236 Constraints of System Restoration 2256.1 Physical Constraints During Restoration 2256.1.1 Generating Unit Start‐Up 2256.1.2 System Sectionalizing and Reconfiguration 2306.1.3 Load Restoration 2336.2 Electromagnetic Transients During System Restoration 2356.2.1 Generator Self‐Excitation 2376.2.2 Switching Overvoltage 2376.2.3 Resonant Overvoltage in the Case of Energizing No‐Load Transformer 2426.2.4 Impact of Magnetizing Inrush Current on Transformer 2456.2.5 Voltage and Frequency Analysis in Picking up Load 247References 2517 Restoration Methodology and Implementation Algorithms 2557.1 Algorithms for Generating Unit Start‐Up 2557.1.1 A General Bilevel Framework 2557.1.2 Algorithms for the Primary Problem 2607.1.3 Algorithms for the Second Problem 2657.2 Algorithms for Load Restoration 2697.2.1 Estimate Operational Region Bound 2717.2.2 Formulate MINLR Model to Maximize Load Pickup 2727.2.3 Branch‐and‐Cut Solver: Design and Justification 2757.2.4 Selection of Branching Methods 2787.3 Case Studies 2787.3.1 Illustrative Example for Restoring Generating Units 2787.3.2 Optimal Load Restoration Strategies for RTS 24‐Bus System 2837.3.3 Optimal Load Restoration Strategies for IEEE 118‐Bus System 287References 2918 Renewable and Energy Storage in System Restoration 2958.1 Planning of Renewable Generators in System Restoration 2958.1.1 Renewables for System Restoration 2958.1.2 The Offline Restoration Tool Using Renewable Energy Resources 2968.1.3 System Restoration with Renewables’ Participation 2988.2 Operation and Control of Renewable Generators in System Restoration 3058.2.1 Prerequisites of Type 3 WTs for System Restoration 3078.2.2 Problem Setup of Type 3 WTs for System Restoration 3088.2.3 Black‐Starting Control and Sequence of Type 3 WTs 3148.2.4 Autonomous Frequency Mechanism of a Type 3 WT-Based Stand‐Alone System 3178.2.5 Simulation Study 3208.3 Energy Storage in System Restoration 3238.3.1 Pumped‐Storage Hydro Units in Restoration 3238.3.2 Batteries for System Restoration 3328.3.3 Electric Vehicles in System Restoration 340References 3519 Emerging Technologies in System Restoration 3579.1 Applications of FACTS and HVDC 3579.1.1 LCC‐HVDC Technology for System Restoration 3579.1.2 VSC‐HVDC Technology for System Restoration 3639.1.3 FACTS Technology for System Restoration 3709.2 Applications of PMUs 3769.2.1 Review of PMU 3769.2.2 System Restoration with PMU Measurements 3789.3 Microgrid in System Restoration 3859.3.1 Microgrid‐Based Restoration 3859.3.2 Demonstration and Practice 388References 39310 Black-Start Capability Assessment and Optimization 39910.1 Background of Black Start 39910.1.1 Definition of Black Start 39910.1.2 Constraints During BS 40010.1.3 BS Service Procurement 40110.1.4 Power System Restoration Procedure 40310.2 BS Capability Assessment 40410.2.1 Installation Criteria of New BS Generators 40410.2.2 Optimal Installation Strategy of BS Capability 40710.2.3 Examples 40810.3 Optimal BS Capability 41110.3.1 Problem Formulation 41110.3.2 Solution Algorithm 41810.3.3 Examples 421References 431Index 433