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 xv

Preface xvii

Acknowledgments xxiii

Part I Introduction 1

1 Introduction 3

1.1 Power Grid and Natural Disasters 3

1.2 Power Grid Resilience 4

1.2.1 Definitions 4

1.2.2 Importance and Benefits 6

1.2.2.1 Dealing withWeather-Related Disastrous Events 6

1.2.2.2 Facilitating the Integration of Renewable Energy Sources 7

1.2.2.3 Dealing with Cybersecurity-Related Events 8

1.2.3 Challenges 9

1.3 Resilience Enhancement Against Disasters 12

1.3.1 Preparedness Prior to Disasters 12

1.3.1.1 Component-Level Resilience Enhancement 13

1.3.1.2 System-Level Resilience Enhancement 14

1.3.2 Response as Disasters Unfold 14

1.3.2.1 System State Acquisition 15

1.3.2.2 Controlled Separation 16

1.3.3 Recovery After Disasters 17

1.3.3.1 Conventional Recovery Process 17

1.3.3.2 Microgrids for Electric Service Recovery 18

1.3.3.3 Distribution Grid Topology Reconfiguration 18

1.4 Coordination and Co-Optimization 20

1.5 Focus of This Book 22

1.6 Summary 23

References 23

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Part II Preparedness Prior to a Natural Disaster 35

2 Preventive Maintenance to Enhance Grid Reliability 37

2.1 Component- and System-Level Deterioration Model 37

2.1.1 Component-Level Deterioration Transition Probability 38

2.1.2 System-Level Deterioration Transition Probability 40

2.1.3 Mathematical Model without Harsh External Conditions 40

2.2 Preventive Maintenance in Consideration of Disasters 41

2.2.1 Potential Disasters Influencing Preventive Maintenance 41

2.2.2 Preventive Maintenance Model with Disasters Influences 42

2.2.2.1 Probabilistic Model of Repair Delays Caused By Harsh External

Conditions 42

2.2.2.2 Activity Vectors Corresponding to Repair Delays 42

2.2.2.3 Expected Cost 43

2.3 Solution Algorithms 44

2.3.1 Backward Induction 44

2.3.2 Search Space Reduction Method 44

2.4 Case Studies 45

2.4.1 Data Description 45

2.4.2 Case I: Verification of the Proposed Model 45

2.4.2.1 Verifying the Model Using Monte Carlo Simulations 46

2.4.2.2 Selection of Optimal Maintenance Activities 47

2.4.2.3 Influences of Harsh External Conditions on Maintenance 48

2.4.3 Case II: Results Simulating the Zhejiang Electric Power Grid 48

2.5 Summary and Conclusions 51

Nomenclature 52

References 53

3 Preallocating Emergency Resources to Enhance Grid

Survivability 55

3.1 Emergency Resources of Grids against Disasters 55

3.2 Mobile Emergency Generators and Grid Survivability 58

3.2.1 Microgrid Formation 59

3.2.2 Preallocation and Real-Time Allocation 59

3.2.3 Coordination with Conventional Restoration Procedures 60

3.3 Preallocation Optimization of Mobile Emergency Generators 61

3.3.1 A Two-Stage Stochastic Optimization Model 61

3.3.2 Availability of Mobile Emergency Generators 66

3.3.3 Connection of Mobile Emergency Generators 66

3.3.4 Coordination of Multiple Flexibility in Microgrids 67

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3.4 Solution Algorithms 67

3.4.1 Scenario Generation and Reduction 68

3.4.2 Dijkstra's Shortest-Path Algorithm 69

3.4.3 Scenario Decomposition Algorithm 69

3.5 Case Studies 70

3.5.1 Test System Introduction 70

3.5.2 Demonstration of the Proposed Dispatch Method 71

3.5.3 Capacity Utilization Rate 73

3.5.4 Importance of Considering Traffic Issue and Preallocation 75

3.5.5 Computational Efficiency 76

3.6 Summary and Conclusions 77

Nomenclature 78

References 80

4 Grid Automation Enabling Prompt Restoration 85

4.1 Smart Grid and Automation Systems 85

4.2 Distribution System Automation and Restoration 87

4.3 Prompt Restoration with Remote-Controlled Switches 89

4.4 Remote-Controlled Switch Allocation Models 91

4.4.1 Minimizing Customer Interruption Cost 91

4.4.2 Minimizing System Average Interruption Duration Index 93

4.4.3 Maximizing System Restoration Capability 94

4.5 Solution Method 95

4.5.1 Practical Candidate Restoration Strategies 95

4.5.2 Model Transformation 99

4.5.3 Linearization and Simplification Techniques 100

4.5.4 Overall Solution Process 100

4.6 Case Studies 102

4.6.1 Illustration on a Small Test System 102

4.6.1.1 Results of the CIC-oriented Model 102

4.6.1.2 Results of the SAIDI-oriented Model 103

4.6.1.3 Results of the RL-oriented Model 105

4.6.1.4 Comparisons 105

4.6.2 Results on a Large Test System 106

4.7 Impacts of Remote-Controlled Switch Malfunction 109

4.8 Consideration of Distributed Generations 110

4.9 Summary and Conclusions 111

Nomenclature of RCS-Restoration Models 112

Nomenclature of RCS Allocation Models 113

References 113

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Part III Response as a Natural Disaster Unfolds 119

5 Security Region-Based Operational Point Analysis for

Resilience Enhancement 121

5.1 Resilience-Oriented Operational Strategies 121

5.2 Security Region during an Unfolding Disaster 123

5.2.1 Sequential Security Region 123

5.2.2 Uncertain Varying System Topology Changes 125

5.3 Operational Point Analysis Resilience Enhancement 126

5.3.1 Sequential Security Region 126

5.3.2 Sequential Security Region with Uncertain Varying Topology

Changes 127

5.3.3 Mapping System Topology Changes 129

5.3.4 Bilevel Optimization Model 130

5.3.5 Solution Process 131

5.4 Case Studies 132

5.5 Summary and Conclusions 138

Nomenclature 138

References 140

6 Proactive Resilience Enhancement Strategy for Transmission

Systems 143

6.1 Proactive Strategy Against ExtremeWeather Events 143

6.2 System States Caused by Unfolding Disasters 145

6.2.1 Component Failure Rate 146

6.2.2 System States on Disasters' Trajectories 146

6.2.3 Transition Probabilities Between Different System States 147

6.3 Sequentially Proactive Operation Strategy 148

6.3.1 Sequential Decision Processes 148

6.3.2 Sequentially Proactive Operation Strategy Constraints 148

6.3.3 Linear Scalarization of the Model 150

6.3.4 Case Studies 152

6.3.4.1 IEEE 30-Bus System 152

6.3.4.2 A Practical Power Grid System 156

6.4 Summary and Conclusions 159

Nomenclature 160

References 162

7 Markov Decision Process-Based Resilience Enhancement for

Distribution Systems 165

7.1 Real-Time Response Against Unfolding Disasters 165

7.2 Disasters' Influences on Distribution Systems 167

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7.2.1 Markov States on Disasters' Trajectories 167

7.2.2 Transition Probability Between Markov States 169

7.3 Markov Decision Processes-Based Optimization Model 169

7.3.1 Markov Decision Processes-based Recursive Model 169

7.3.2 Operational Constraints 170

7.3.2.1 Radiality Constraint 170

7.3.2.2 Repair Constraint 170

7.3.2.3 Power Flow Constraint 171

7.3.2.4 Power Balance Constraint 171

7.3.2.5 Line Capacity Constraint 171

7.3.2.6 Voltage Constraint 172

7.4 Solution Algorithms - Approximate Dynamic Programming 172

7.4.1 Solution Challenges 172

7.4.2 Post-decision States 174

7.4.3 Forward Dynamic Algorithm 174

7.4.4 Proposed Model Reformulation 175

7.4.5 Iteration Process 177

7.5 Case Studies 177

7.5.1 IEEE 33-Bus System 177

7.5.1.1 Data Description 177

7.5.1.2 Estimated Values of Post-Decision States 178

7.5.1.3 Dispatch Strategies with Estimated Values of Post-Decision States 180

7.5.2 IEEE 123-Bus System 181

7.5.2.1 Data Description 181

7.5.2.2 Simulated Results 181

7.6 Summary and Conclusions 183

Nomenclature 184

References 186

Part IV Recovery After a Natural Disaster 189

8 Microgrids with Flexible Boundaries for Service

Restoration 191

8.1 Using Microgrids in Service Restoration 191

8.2 Dynamically Formed Microgrids 194

8.2.1 Flexible Boundaries in Microgrid Formation Optimization 194

8.2.2 Radiality Constraints and Topological Flexibility 195

8.3 Mathematical Formulation of Radiality Constraints 198

8.3.1 Loop-Eliminating Model 200

8.3.2 Path-Based Model 200

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8.3.3 Single-Commodity Flow-Based Model 200

8.3.4 Parent-Child Node Relation-Based Model 201

8.3.5 Primal and Dual Graph-Based Model 201

8.3.6 Spanning Forest-Based Model 201

8.4 Adaptive Microgrid Formation for Service Restoration 202

8.4.1 Formulation and Validity 202

8.4.2 Tightness and Compactness 205

8.4.3 Applicability and Application 207

8.5 Case Studies 211

8.5.1 Illustration on a Small Test System 211

8.5.2 Results on a Large Test System 215

8.5.3...