Shunbo Lei, PhD, is an Assistant Professor in the School of Science and Engineering at the Chinese University of Hong Kong, Shenzhen, China. Chong Wang, PhD, is a Professor in the College of Energy and Electrical Engineering at Hohai University, Nanjing, China. Yunhe Hou, PhD, is an Associate Professor in the Department of Electrical and Electronic Engineering at the University of Hong Kong, Pokfulam, Hong Kong.

• About the Authors xvPreface xviiAcknowledgments xxiiiPart I Introduction 11 Introduction 31.1 Power Grid and Natural Disasters 31.2 Power Grid Resilience 41.2.1 Definitions 41.2.2 Importance and Benefits 61.2.2.1 Dealing withWeather-Related Disastrous Events 61.2.2.2 Facilitating the Integration of Renewable Energy Sources 71.2.2.3 Dealing with Cybersecurity-Related Events 81.2.3 Challenges 91.3 Resilience Enhancement Against Disasters 121.3.1 Preparedness Prior to Disasters 121.3.1.1 Component-Level Resilience Enhancement 131.3.1.2 System-Level Resilience Enhancement 141.3.2 Response as Disasters Unfold 141.3.2.1 System State Acquisition 151.3.2.2 Controlled Separation 161.3.3 Recovery After Disasters 171.3.3.1 Conventional Recovery Process 171.3.3.2 Microgrids for Electric Service Recovery 181.3.3.3 Distribution Grid Topology Reconfiguration 181.4 Coordination and Co-Optimization 201.5 Focus of This Book 221.6 Summary 23References 23Trim Size: 152mm x 229mm Single Column Lei801474 ftoc.tex V1 - 10/31/2022 4:04pm Page viii[1][1] [1][1]viii ContentsPart II Preparedness Prior to a Natural Disaster 352 Preventive Maintenance to Enhance Grid Reliability 372.1 Component- and System-Level Deterioration Model 372.1.1 Component-Level Deterioration Transition Probability 382.1.2 System-Level Deterioration Transition Probability 402.1.3 Mathematical Model without Harsh External Conditions 402.2 Preventive Maintenance in Consideration of Disasters 412.2.1 Potential Disasters Influencing Preventive Maintenance 412.2.2 Preventive Maintenance Model with Disasters Influences 422.2.2.1 Probabilistic Model of Repair Delays Caused By Harsh ExternalConditions 422.2.2.2 Activity Vectors Corresponding to Repair Delays 422.2.2.3 Expected Cost 432.3 Solution Algorithms 442.3.1 Backward Induction 442.3.2 Search Space Reduction Method 442.4 Case Studies 452.4.1 Data Description 452.4.2 Case I: Verification of the Proposed Model 452.4.2.1 Verifying the Model Using Monte Carlo Simulations 462.4.2.2 Selection of Optimal Maintenance Activities 472.4.2.3 Influences of Harsh External Conditions on Maintenance 482.4.3 Case II: Results Simulating the Zhejiang Electric Power Grid 482.5 Summary and Conclusions 51Nomenclature 52References 533 Preallocating Emergency Resources to Enhance GridSurvivability 553.1 Emergency Resources of Grids against Disasters 553.2 Mobile Emergency Generators and Grid Survivability 583.2.1 Microgrid Formation 593.2.2 Preallocation and Real-Time Allocation 593.2.3 Coordination with Conventional Restoration Procedures 603.3 Preallocation Optimization of Mobile Emergency Generators 613.3.1 A Two-Stage Stochastic Optimization Model 613.3.2 Availability of Mobile Emergency Generators 663.3.3 Connection of Mobile Emergency Generators 663.3.4 Coordination of Multiple Flexibility in Microgrids 67Trim Size: 152mm x 229mm Single Column Lei801474 ftoc.tex V1 - 10/31/2022 4:04pm Page ix[1][1] [1][1]Contents ix3.4 Solution Algorithms 673.4.1 Scenario Generation and Reduction 683.4.2 Dijkstra’s Shortest-Path Algorithm 693.4.3 Scenario Decomposition Algorithm 693.5 Case Studies 703.5.1 Test System Introduction 703.5.2 Demonstration of the Proposed Dispatch Method 713.5.3 Capacity Utilization Rate 733.5.4 Importance of Considering Traffic Issue and Preallocation 753.5.5 Computational Efficiency 763.6 Summary and Conclusions 77Nomenclature 78References 804 Grid Automation Enabling Prompt Restoration 854.1 Smart Grid and Automation Systems 854.2 Distribution System Automation and Restoration 874.3 Prompt Restoration with Remote-Controlled Switches 894.4 Remote-Controlled Switch Allocation Models 914.4.1 Minimizing Customer Interruption Cost 914.4.2 Minimizing System Average Interruption Duration Index 934.4.3 Maximizing System Restoration Capability 944.5 Solution Method 954.5.1 Practical Candidate Restoration Strategies 954.5.2 Model Transformation 994.5.3 Linearization and Simplification Techniques 1004.5.4 Overall Solution Process 1004.6 Case Studies 1024.6.1 Illustration on a Small Test System 1024.6.1.1 Results of the CIC-oriented Model 1024.6.1.2 Results of the SAIDI-oriented Model 1034.6.1.3 Results of the RL-oriented Model 1054.6.1.4 Comparisons 1054.6.2 Results on a Large Test System 1064.7 Impacts of Remote-Controlled Switch Malfunction 1094.8 Consideration of Distributed Generations 1104.9 Summary and Conclusions 111Nomenclature of RCS-Restoration Models 112Nomenclature of RCS Allocation Models 113References 113Trim Size: 152mm x 229mm Single Column Lei801474 ftoc.tex V1 - 10/31/2022 4:04pm Page x[1][1] [1][1]x ContentsPart III Response as a Natural Disaster Unfolds 1195 Security Region-Based Operational Point Analysis forResilience Enhancement 1215.1 Resilience-Oriented Operational Strategies 1215.2 Security Region during an Unfolding Disaster 1235.2.1 Sequential Security Region 1235.2.2 Uncertain Varying System Topology Changes 1255.3 Operational Point Analysis Resilience Enhancement 1265.3.1 Sequential Security Region 1265.3.2 Sequential Security Region with Uncertain Varying TopologyChanges 1275.3.3 Mapping System Topology Changes 1295.3.4 Bilevel Optimization Model 1305.3.5 Solution Process 1315.4 Case Studies 1325.5 Summary and Conclusions 138Nomenclature 138References 1406 Proactive Resilience Enhancement Strategy for TransmissionSystems 1436.1 Proactive Strategy Against ExtremeWeather Events 1436.2 System States Caused by Unfolding Disasters 1456.2.1 Component Failure Rate 1466.2.2 System States on Disasters’ Trajectories 1466.2.3 Transition Probabilities Between Different System States 1476.3 Sequentially Proactive Operation Strategy 1486.3.1 Sequential Decision Processes 1486.3.2 Sequentially Proactive Operation Strategy Constraints 1486.3.3 Linear Scalarization of the Model 1506.3.4 Case Studies 1526.3.4.1 IEEE 30-Bus System 1526.3.4.2 A Practical Power Grid System 1566.4 Summary and Conclusions 159Nomenclature 160References 1627 Markov Decision Process-Based Resilience Enhancement forDistribution Systems 1657.1 Real-Time Response Against Unfolding Disasters 1657.2 Disasters’ Influences on Distribution Systems 167Trim Size: 152mm x 229mm Single Column Lei801474 ftoc.tex V1 - 10/31/2022 4:04pm Page xi[1][1] [1][1]Contents xi7.2.1 Markov States on Disasters’ Trajectories 1677.2.2 Transition Probability Between Markov States 1697.3 Markov Decision Processes-Based Optimization Model 1697.3.1 Markov Decision Processes-based Recursive Model 1697.3.2 Operational Constraints 1707.3.2.1 Radiality Constraint 1707.3.2.2 Repair Constraint 1707.3.2.3 Power Flow Constraint 1717.3.2.4 Power Balance Constraint 1717.3.2.5 Line Capacity Constraint 1717.3.2.6 Voltage Constraint 1727.4 Solution Algorithms – Approximate Dynamic Programming 1727.4.1 Solution Challenges 1727.4.2 Post-decision States 1747.4.3 Forward Dynamic Algorithm 1747.4.4 Proposed Model Reformulation 1757.4.5 Iteration Process 1777.5 Case Studies 1777.5.1 IEEE 33-Bus System 1777.5.1.1 Data Description 1777.5.1.2 Estimated Values of Post-Decision States 1787.5.1.3 Dispatch Strategies with Estimated Values of Post-Decision States 1807.5.2 IEEE 123-Bus System 1817.5.2.1 Data Description 1817.5.2.2 Simulated Results 1817.6 Summary and Conclusions 183Nomenclature 184References 186Part IV Recovery After a Natural Disaster 1898 Microgrids with Flexible Boundaries for ServiceRestoration 1918.1 Using Microgrids in Service Restoration 1918.2 Dynamically Formed Microgrids 1948.2.1 Flexible Boundaries in Microgrid Formation Optimization 1948.2.2 Radiality Constraints and Topological Flexibility 1958.3 Mathematical Formulation of Radiality Constraints 1988.3.1 Loop-Eliminating Model 2008.3.2 Path-Based Model 200Trim Size: 152mm x 229mm Single Column Lei801474 ftoc.tex V1 - 10/31/2022 4:04pm Page xii[1][1] [1][1]xii Contents8.3.3 Single-Commodity Flow-Based Model 2008.3.4 Parent–Child Node Relation-Based Model 2018.3.5 Primal and Dual Graph-Based Model 2018.3.6 Spanning Forest-Based Model 2018.4 Adaptive Microgrid Formation for Service Restoration 2028.4.1 Formulation and Validity 2028.4.2 Tightness and Compactness 2058.4.3 Applicability and Application 2078.5 Case Studies 2118.5.1 Illustration on a Small Test System 2118.5.2 Results on a Large Test System 2158.5.3 LinDistFlow Model Accuracy 2198.6 Summary and Conclusions 2198.A.1 Proof of Theorem 8.1 2208.A.2 Proof of Proposition 8.1 220Nomenclature of Spanning Tree Constraints 221Nomenclature of MG Formation Model 221References 2229 Microgrids with Mobile Power Sources for ServiceRestoration 2279.1 Grid Survivability and Recovery with Mobile Power Sources 2279.2 Routing and Scheduling Mobile Power Sources in Microgrids 2309.3 Mobile Power Sources and Supporting Facilities 2339.3.1 Availability 2339.3.2 Grid-Forming Functions 2349.3.3 Cost-Effectiveness 2349.4 A Two-Stage Dispatch Framework 2359.4.1 Proactive Pre-Dispatch 2359.4.2 Dynamic Routing and Scheduling 2399.5 Solution Method 2439.5.1 Column-and-Constraint Generation Algorithm 2439.5.2 Linearization Techniques 2459.6 Case Studies 2459.6.1 Illustration on a Small Test System 2469.6.1.1 Results of MPS Proactive Pre-positioning 2469.6.1.2 Results of MPS Dynamic Dispatch 2479.6.2 Results on a Large Test System 2519.7 Summary and Conclusions 255Nomenclature 255References 257Trim Size: 152mm x 229mm Single Column Lei801474 ftoc.tex V1 - 10/31/2022 4:04pm Page xiii[1][1] [1][1]Contents xiii10 Co-Optimization of Grid Flexibilities in RecoveryLogistics 26110.1 Post-Disaster Recovery Logistics of Grids 26110.1.1 Power Infrastructure Recovery 26210.1.2 Microgrid-Based Service Restoration 26310.1.3 A Co-Optimization Approach 26410.2 Flexibility Resources in Grid Recovery Logistics 26510.2.1 Routing and Scheduling of Repair Crews 26510.2.2 Routing and Scheduling of Mobile Power Sources 26810.2.3 Grid Reconfiguration and Operation 27110.3 Co-Optimization of Flexibility Resources 27710.4 Solution Method 28010.4.1 Pre-assigning Minimal Repair Tasks 28010.4.2 Selecting Candidate Nodes to Connect Mobile Power Sources 28110.4.3 Linearization Techniques 28310.5 Case Studies 28410.5.1 Illustration on a Small Test System 28410.5.2 Results on a Large Test System 28710.5.3 Computational Efficiency 29010.5.4 LinDistFlow Model Accuracy 29210.6 Summary and Conclusions 29310.A.1 Proof of Proposition 10.1 293References 294Index 301