Mathaios Panteli, Assistant Professor, University of Cyprus. Rodrigo Moreno, Assistant Professor, University of Chile. Dimitris Trakas, Senior Researcher, National Technical University of Athens, Greece. Magnus Jamieson, Research Associate, Imperial College London, UK. Pierluigi Mancarella, Chair Professor of Electrical Power Systems, University of Melbourne, Australia, and Professor of Smart Energy Systems, University of Manchester, UK. Goran Strbac, Chair Professor in Electrical Energy Systems, Imperial College London, UK. Nikos Hatziargyriou, Professor in Power Systems, National Technical University of Athens, Greece.

• About the Authors xiForeword by Professor Chongqing Kang xvForeword by Professor Ian Dobson xviiPreface xix1 From Reliability to Resilience 11.1 Why Power System Resilience? 11.2 The Historical Approaches to Power System Reliability 31.2.1 The Historical N-k Network Security Criterion 31.2.2 The More Advanced Probabilistic Network Security 31.3 Need for a (Tail)Risk-Aware Approach 41.4 Inspiration from Other Economic and Engineering Areas 51.4.1 Risk Hedging and Portfolio Optimization 51.4.2 Risk-Aware Design in Structural and Civil Engineering 61.5 From Reliability to Resilience Paradigm 71.5.1 Key Differentiators Between Reliability and Resilience 71.5.2 Expanding Resilience Practices 81.5.2.1 Broadening the Scope of Contingencies 81.5.2.2 Focusing on High-Risk Scenarios 81.5.2.3 Incorporating Environmental Interactions 81.5.2.4 Tailoring Strategies to Natural Threats 81.5.2.5 Integrating Diverse Measures and Technologies 91.5.2.6 Emphasizing Dynamics and Recovery 91.6 Fundamentals of Power System Resilience 91.6.1 Contribution to the Field 101.6.2 Closing Remarks 10References 112 Conceptualizing and Contextualizing Power Grid Resilience 132.1 Shocks and Stresses on Critical Power Infrastructure 132.2 Defining Power System Resilience 152.3 Resilience Capacities and Features 182.4 Comparing and Clarifying Reliability and Resilience 202.5 Conceptualizing Power System Resilience to External Shocks 222.6 Domains of Resilience 262.6.1 Infrastructure Resilience 262.6.2 Operational Resilience 272.6.3 Organizational Resilience 272.6.4 Community Resilience 27References 283 System Resilience Assessment and Quantification 313.1 Needed Resilience Metrics for Power Systems 313.2 Quantifying the Resilience Trapezoid 323.2.1 The FLEP and Area Metric Systems 323.2.2 Fragility-Driven Resilience Assessment Against Windstorms 353.3 CVaR-Driven Resilience Assessment 433.3.1 Illustrative Example of CVaR Resilience Assessment Against Wind Events 443.4 AC Cascading Modeling for Resilience Applications 453.4.1 Recursive Application of Protection Mechanisms 483.4.2 Obtaining a Solvable PF 503.4.3 Implementation of Protection Mechanisms 503.4.3.1 Cascade Visualization 543.4.4 Integration into Resilience Metric Frameworks 54References 584 Addressing Data Granularity and Ambiguity 614.1 Understanding Outage Models on Power Systems 614.2 Homogeneous Versus Distributed Representations of Failure Hazard on Overhead Lines 664.2.1 Homogeneous Representations of Outage Risk on Lines 674.3 Distributed Failure Risk Representation on Lines 674.4 Method for Representing Spatial Risk of a Natural Hazard 704.5 Data Acquisition 704.5.1 Calculating Exposure of System to Natural Hazards 714.5.2 Modeling Failure Probability 734.5.3 Correcting Wind Speed Data for Different Heights of Asset 764.5.4 Interpolation of Datasets for the Purposes of Resilience Studies 774.5.5 A Tractable Method for Calculating Wind Power Outputs in Extreme Wind Events 784.5.6 A Case Study Using Demonstrated Methods on the Northern Scottish Transmission System 794.6 Exercises 844.7 Correlated Natural Hazards 864.8 Incorporating Imprecise Fragility Curves in Decision-Making Models 904.9 Summary 91Acknowledgments 92Reference 925 Resilient Investment Planning 955.1 Network Investment Decisions: Unraveling the Planner’s Trilemma 955.1.1 Expanding and Hardening Solutions 955.1.2 Digitalized, Non-Wire and Smart Grid Solutions 965.1.3 The Resilience Enhancement Trilemma 975.2 Resilience and Risk Metrics for Risk-Averse Decision-Making 985.2.1 A Probabilistic Risk Metric 1005.2.2 Risk Versus Resilience Metrics 1015.2.3 Dependencies and Common Mode 1015.2.4 Example of Probability Capacity Tables Accounting for Dependencies in a Double Circuit 1025.2.5 Deterministic or “Robust” Approach to Risk 1035.2.6 Distributionally Robust Approach to Risk 1045.3 Mathematical Frameworks to Plan Resilient Grids 1045.3.1 Possible Theoretical Formulations: From Robust to Stochastic Network Planning 1045.3.1.1 Two-Stage Framework 1045.3.1.2 Multi-Stage Framework with Two Layers of Uncertainty 1055.3.2 CVaR Formulation 1065.3.3 Optimization via Simulation Approach: A Two-Stage Stochastic Model 1065.3.4 Advanced Resilient Investment Planning Models 1095.4 Merging Resilience and Reliability Criteria for Practical Decisions 1105.4.1 Illustrative Case Study 1105.4.2 Reliability I: Adequacy 1105.4.3 Reliability II: Security 1105.4.4 Resilience 1115.4.5 Combining Reliability and Resilience 1135.5 Realistic Application to Earthquakes in Chile 1135.5.1 Case Study Description 1145.5.2 Results: Portfolio Solutions for Resilience Enhancement 1155.6 Main Grid Resilience Investments Versus DER 1165.6.1 A Suitable Methodology to Design DER Portfolios Against Wildfires 1165.6.2 Illustrative Case Study Example 1185.6.3 The Classic N–1 Design 1195.6.4 The Resilient Design 1205.6.5 The Actual Risks Associated with the Current Security Standards 1205.7 Investment Versus Operational Measures 1215.7.1 A Comment on Resilience and CVaR Effects on Portfolio Diversification 1225.8 Fairness Considerations in Resilience 1225.9 Beyond Networks: Long-Term Duration Energy Storage to Enhance Future Energy System Resilience Against Prolonged Low Output of RES 124References 1276 Operational Resilience Planning 131Nomenclature 1316.1 Introduction 1326.2 Smart Operational Measures 1356.3 Preventive Unit Commitment to Enhance Power System Resilience Under Extreme Weather Events 1366.3.1 Resilience Preventive Unit Commitment Using Robust Optimization 1386.3.1.1 Mathematical Formulation 1386.3.1.2 Problem Reformulation and Solution Algorithm 1406.3.1.3 Case Study Applications 1416.3.2 Machine Learning Techniques to Deal with Multiple Line Failures Under Extreme Events 1456.3.2.1 Mathematical Formulation 1456.3.2.2 Machine Learning Assisted Stochastic Unit Commitment 1476.3.2.3 Case Study Applications 1486.4 Defensive Islanding to Enhance Power System Resilience Under Extreme Weather Events 1516.4.1 Defensive Islanding Algorithm 1516.4.2 Approach for Determining when to Apply Defensive Islanding 1536.4.3 Case Study Applications 1546.5 Resilience Enhancement in Low-Carbon, Low-Inertia Power Systems 1606.5.1 Dynamic Network Model 1616.5.2 Mathematical Formulation 1626.5.3 Case Study Applications 1636.5.3.1 Base Case Results 1646.5.3.2 SECOPF Results 1656.6 Appendix 1676.6.1 Reformulation and Solution Algorithm of Tri-level Problems 1676.6.2 Solution Algorithm 168References 1687 Resilience by Distributed Energy Resources and Microgrids 1777.1 Local and Bulk System Resilience 1777.1.1 Overview of Microgrids 1787.1.2 Resilient Decarbonization of Multi-Energy Microgrids 1797.1.3 Electrified Transport Sector and Mobile Sources Enhancing Resilience 1817.2 Resilience Support by Real-World Microgrids 1817.2.1 Princeton Microgrid Against Hurricanes – United States 1817.2.2 The Sendai Microgrid During and After the Tsunami and Large-Scale Earthquake – Japan 1827.2.3 Blue Lake Rancheria Microgrid Against Wildfires – United States 1827.2.4 Texas Microgrids Against Winter Storms – United States 1837.2.5 Louisiana Microgrids Against Hurricanes – United States 1847.2.6 Microgrids Against Earthquakes – Haiti 1857.2.7 The Kythnos Microgrid During Natural Disasters – Greece 1857.2.8 Support from Mobile Generators – Ad Hoc Microgrids Against Wildfires – Greece 1867.2.9 Support from Local Generation Islanded Operation of Constitución Against Wildfires – Chile 1867.3 DER/Microgrids Role in Strengthening Resilience 1877.3.1 Resilience Enhancement at All Power System Levels 1877.3.2 Resilience Enhancement in All Resilience Phases 1877.4 Preventive and Corrective Microgrid Formation 1897.4.1 The Base Model 1897.4.1.1 Partitioning Constraints 1907.4.1.2 Operating Constraints 1947.4.1.3 Objective Function 1947.4.1.4 Numerical Results 1957.4.2 Advances of the Base Model 1977.4.2.1 Reformulating the Partitioning Constraints 1977.4.2.2 Further Advances in MGs Formulation 1997.4.2.3 Integration with DER Scheduling 2007.5 Microgrids for Resilience-Oriented Restoration 2017.5.1 Microgrids Aided Distribution System Restoration 2017.5.1.1 Operating Constraints 2027.5.1.2 Connectivity and Sequence Constraints 2037.5.1.3 Topological Constraints 2047.5.1.4 Initial Condition Constraints 2047.5.1.5 Optimization Formulation 2047.5.2 Restoration of a Microgrid 2057.5.2.1 Microgrid Restoration Sequence 2057.5.2.2 Protection Considerations 2067.5.2.3 Decentralized Techniques 2067.6 Resilience-Oriented Preventive and Emergency DER Scheduling 2077.6.1 Problem Formulation 2077.6.2 Study Case Application 2097.6.2.1 Test Network and Simulation Data 2097.6.2.2 Operation Against Approaching Wildfire 211References 2158 Resilience of Low-Carbon Power Systems: Standards, Market, Regulatory, and Policy Aspects 2218.1 Introduction 2218.2 Weather and Low-Carbon Grid Reliability 2218.3 Weather and Low-Carbon Grid Resilience 2228.4 From Reliability to Resilience in Low-Carbon Grids: Need for New Security Standards 2238.5 Toward a New Regulatory Framework for Resilience 2258.6 Measuring Power System Resilience 2278.7 The Economics of Resilience: “Value of Customer Resilience” and Risk Aversion 2298.8 The Economics of Resilience: Cost–Benefit Analysis and Risk Aversion 2328.9 The Economics of Resilience: Cost-Effectiveness Analysis 2328.10 Regulation, Policy, and Markets: Who Should Provide Resilience? 2338.11 Regulation, Policy and Markets: Who Should Pay for Resilience? 2358.12 Resilience, Decarbonization Policies, and Digitalization Paradigm 2358.13 A Regulatory Perspective on Resilience: Final Considerations 237References 238Index 241

Mathaios Panteli, Assistant Professor, University of Cyprus. Rodrigo Moreno, Assistant Professor, University of Chile. Dimitris Trakas, Senior Researcher, National Technical University of Athens, Greece. Magnus Jamieson, Research Associate, Imperial College London, UK. Pierluigi Mancarella, Chair Professor of Electrical Power Systems, University of Melbourne, Australia, and Professor of Smart Energy Systems, University of Manchester, UK. Goran Strbac, Chair Professor in Electrical Energy Systems, Imperial College London, UK. Nikos Hatziargyriou, Professor in Power Systems, National Technical University of Athens, Greece.

• About the Authors xiForeword by Professor Chongqing Kang xvForeword by Professor Ian Dobson xviiPreface xix1 From Reliability to Resilience 11.1 Why Power System Resilience? 11.2 The Historical Approaches to Power System Reliability 31.2.1 The Historical N-k Network Security Criterion 31.2.2 The More Advanced Probabilistic Network Security 31.3 Need for a (Tail)Risk-Aware Approach 41.4 Inspiration from Other Economic and Engineering Areas 51.4.1 Risk Hedging and Portfolio Optimization 51.4.2 Risk-Aware Design in Structural and Civil Engineering 61.5 From Reliability to Resilience Paradigm 71.5.1 Key Differentiators Between Reliability and Resilience 71.5.2 Expanding Resilience Practices 81.5.2.1 Broadening the Scope of Contingencies 81.5.2.2 Focusing on High-Risk Scenarios 81.5.2.3 Incorporating Environmental Interactions 81.5.2.4 Tailoring Strategies to Natural Threats 81.5.2.5 Integrating Diverse Measures and Technologies 91.5.2.6 Emphasizing Dynamics and Recovery 91.6 Fundamentals of Power System Resilience 91.6.1 Contribution to the Field 101.6.2 Closing Remarks 10References 112 Conceptualizing and Contextualizing Power Grid Resilience 132.1 Shocks and Stresses on Critical Power Infrastructure 132.2 Defining Power System Resilience 152.3 Resilience Capacities and Features 182.4 Comparing and Clarifying Reliability and Resilience 202.5 Conceptualizing Power System Resilience to External Shocks 222.6 Domains of Resilience 262.6.1 Infrastructure Resilience 262.6.2 Operational Resilience 272.6.3 Organizational Resilience 272.6.4 Community Resilience 27References 283 System Resilience Assessment and Quantification 313.1 Needed Resilience Metrics for Power Systems 313.2 Quantifying the Resilience Trapezoid 323.2.1 The FLEP and Area Metric Systems 323.2.2 Fragility-Driven Resilience Assessment Against Windstorms 353.3 CVaR-Driven Resilience Assessment 433.3.1 Illustrative Example of CVaR Resilience Assessment Against Wind Events 443.4 AC Cascading Modeling for Resilience Applications 453.4.1 Recursive Application of Protection Mechanisms 483.4.2 Obtaining a Solvable PF 503.4.3 Implementation of Protection Mechanisms 503.4.3.1 Cascade Visualization 543.4.4 Integration into Resilience Metric Frameworks 54References 584 Addressing Data Granularity and Ambiguity 614.1 Understanding Outage Models on Power Systems 614.2 Homogeneous Versus Distributed Representations of Failure Hazard on Overhead Lines 664.2.1 Homogeneous Representations of Outage Risk on Lines 674.3 Distributed Failure Risk Representation on Lines 674.4 Method for Representing Spatial Risk of a Natural Hazard 704.5 Data Acquisition 704.5.1 Calculating Exposure of System to Natural Hazards 714.5.2 Modeling Failure Probability 734.5.3 Correcting Wind Speed Data for Different Heights of Asset 764.5.4 Interpolation of Datasets for the Purposes of Resilience Studies 774.5.5 A Tractable Method for Calculating Wind Power Outputs in Extreme Wind Events 784.5.6 A Case Study Using Demonstrated Methods on the Northern Scottish Transmission System 794.6 Exercises 844.7 Correlated Natural Hazards 864.8 Incorporating Imprecise Fragility Curves in Decision-Making Models 904.9 Summary 91Acknowledgments 92Reference 925 Resilient Investment Planning 955.1 Network Investment Decisions: Unraveling the Planner’s Trilemma 955.1.1 Expanding and Hardening Solutions 955.1.2 Digitalized, Non-Wire and Smart Grid Solutions 965.1.3 The Resilience Enhancement Trilemma 975.2 Resilience and Risk Metrics for Risk-Averse Decision-Making 985.2.1 A Probabilistic Risk Metric 1005.2.2 Risk Versus Resilience Metrics 1015.2.3 Dependencies and Common Mode 1015.2.4 Example of Probability Capacity Tables Accounting for Dependencies in a Double Circuit 1025.2.5 Deterministic or “Robust” Approach to Risk 1035.2.6 Distributionally Robust Approach to Risk 1045.3 Mathematical Frameworks to Plan Resilient Grids 1045.3.1 Possible Theoretical Formulations: From Robust to Stochastic Network Planning 1045.3.1.1 Two-Stage Framework 1045.3.1.2 Multi-Stage Framework with Two Layers of Uncertainty 1055.3.2 CVaR Formulation 1065.3.3 Optimization via Simulation Approach: A Two-Stage Stochastic Model 1065.3.4 Advanced Resilient Investment Planning Models 1095.4 Merging Resilience and Reliability Criteria for Practical Decisions 1105.4.1 Illustrative Case Study 1105.4.2 Reliability I: Adequacy 1105.4.3 Reliability II: Security 1105.4.4 Resilience 1115.4.5 Combining Reliability and Resilience 1135.5 Realistic Application to Earthquakes in Chile 1135.5.1 Case Study Description 1145.5.2 Results: Portfolio Solutions for Resilience Enhancement 1155.6 Main Grid Resilience Investments Versus DER 1165.6.1 A Suitable Methodology to Design DER Portfolios Against Wildfires 1165.6.2 Illustrative Case Study Example 1185.6.3 The Classic N–1 Design 1195.6.4 The Resilient Design 1205.6.5 The Actual Risks Associated with the Current Security Standards 1205.7 Investment Versus Operational Measures 1215.7.1 A Comment on Resilience and CVaR Effects on Portfolio Diversification 1225.8 Fairness Considerations in Resilience 1225.9 Beyond Networks: Long-Term Duration Energy Storage to Enhance Future Energy System Resilience Against Prolonged Low Output of RES 124References 1276 Operational Resilience Planning 131Nomenclature 1316.1 Introduction 1326.2 Smart Operational Measures 1356.3 Preventive Unit Commitment to Enhance Power System Resilience Under Extreme Weather Events 1366.3.1 Resilience Preventive Unit Commitment Using Robust Optimization 1386.3.1.1 Mathematical Formulation 1386.3.1.2 Problem Reformulation and Solution Algorithm 1406.3.1.3 Case Study Applications 1416.3.2 Machine Learning Techniques to Deal with Multiple Line Failures Under Extreme Events 1456.3.2.1 Mathematical Formulation 1456.3.2.2 Machine Learning Assisted Stochastic Unit Commitment 1476.3.2.3 Case Study Applications 1486.4 Defensive Islanding to Enhance Power System Resilience Under Extreme Weather Events 1516.4.1 Defensive Islanding Algorithm 1516.4.2 Approach for Determining when to Apply Defensive Islanding 1536.4.3 Case Study Applications 1546.5 Resilience Enhancement in Low-Carbon, Low-Inertia Power Systems 1606.5.1 Dynamic Network Model 1616.5.2 Mathematical Formulation 1626.5.3 Case Study Applications 1636.5.3.1 Base Case Results 1646.5.3.2 SECOPF Results 1656.6 Appendix 1676.6.1 Reformulation and Solution Algorithm of Tri-level Problems 1676.6.2 Solution Algorithm 168References 1687 Resilience by Distributed Energy Resources and Microgrids 1777.1 Local and Bulk System Resilience 1777.1.1 Overview of Microgrids 1787.1.2 Resilient Decarbonization of Multi-Energy Microgrids 1797.1.3 Electrified Transport Sector and Mobile Sources Enhancing Resilience 1817.2 Resilience Support by Real-World Microgrids 1817.2.1 Princeton Microgrid Against Hurricanes – United States 1817.2.2 The Sendai Microgrid During and After the Tsunami and Large-Scale Earthquake – Japan 1827.2.3 Blue Lake Rancheria Microgrid Against Wildfires – United States 1827.2.4 Texas Microgrids Against Winter Storms – United States 1837.2.5 Louisiana Microgrids Against Hurricanes – United States 1847.2.6 Microgrids Against Earthquakes – Haiti 1857.2.7 The Kythnos Microgrid During Natural Disasters – Greece 1857.2.8 Support from Mobile Generators – Ad Hoc Microgrids Against Wildfires – Greece 1867.2.9 Support from Local Generation Islanded Operation of Constitución Against Wildfires – Chile 1867.3 DER/Microgrids Role in Strengthening Resilience 1877.3.1 Resilience Enhancement at All Power System Levels 1877.3.2 Resilience Enhancement in All Resilience Phases 1877.4 Preventive and Corrective Microgrid Formation 1897.4.1 The Base Model 1897.4.1.1 Partitioning Constraints 1907.4.1.2 Operating Constraints 1947.4.1.3 Objective Function 1947.4.1.4 Numerical Results 1957.4.2 Advances of the Base Model 1977.4.2.1 Reformulating the Partitioning Constraints 1977.4.2.2 Further Advances in MGs Formulation 1997.4.2.3 Integration with DER Scheduling 2007.5 Microgrids for Resilience-Oriented Restoration 2017.5.1 Microgrids Aided Distribution System Restoration 2017.5.1.1 Operating Constraints 2027.5.1.2 Connectivity and Sequence Constraints 2037.5.1.3 Topological Constraints 2047.5.1.4 Initial Condition Constraints 2047.5.1.5 Optimization Formulation 2047.5.2 Restoration of a Microgrid 2057.5.2.1 Microgrid Restoration Sequence 2057.5.2.2 Protection Considerations 2067.5.2.3 Decentralized Techniques 2067.6 Resilience-Oriented Preventive and Emergency DER Scheduling 2077.6.1 Problem Formulation 2077.6.2 Study Case Application 2097.6.2.1 Test Network and Simulation Data 2097.6.2.2 Operation Against Approaching Wildfire 211References 2158 Resilience of Low-Carbon Power Systems: Standards, Market, Regulatory, and Policy Aspects 2218.1 Introduction 2218.2 Weather and Low-Carbon Grid Reliability 2218.3 Weather and Low-Carbon Grid Resilience 2228.4 From Reliability to Resilience in Low-Carbon Grids: Need for New Security Standards 2238.5 Toward a New Regulatory Framework for Resilience 2258.6 Measuring Power System Resilience 2278.7 The Economics of Resilience: “Value of Customer Resilience” and Risk Aversion 2298.8 The Economics of Resilience: Cost–Benefit Analysis and Risk Aversion 2328.9 The Economics of Resilience: Cost-Effectiveness Analysis 2328.10 Regulation, Policy, and Markets: Who Should Provide Resilience? 2338.11 Regulation, Policy and Markets: Who Should Pay for Resilience? 2358.12 Resilience, Decarbonization Policies, and Digitalization Paradigm 2358.13 A Regulatory Perspective on Resilience: Final Considerations 237References 238Index 241

Mathaios Panteli, Assistant Professor, University of Cyprus. Rodrigo Moreno, Assistant Professor, University of Chile. Dimitris Trakas, Senior Researcher, National Technical University of Athens, Greece. Magnus Jamieson, Research Associate, Imperial College London, UK. Pierluigi Mancarella, Chair Professor of Electrical Power Systems, University of Melbourne, Australia, and Professor of Smart Energy Systems, University of Manchester, UK. Goran Strbac, Chair Professor in Electrical Energy Systems, Imperial College London, UK. Nikos Hatziargyriou, Professor in Power Systems, National Technical University of Athens, Greece.

• About the Authors xiForeword by Professor Chongqing Kang xvForeword by Professor Ian Dobson xviiPreface xix1 From Reliability to Resilience 11.1 Why Power System Resilience? 11.2 The Historical Approaches to Power System Reliability 31.2.1 The Historical N-k Network Security Criterion 31.2.2 The More Advanced Probabilistic Network Security 31.3 Need for a (Tail)Risk-Aware Approach 41.4 Inspiration from Other Economic and Engineering Areas 51.4.1 Risk Hedging and Portfolio Optimization 51.4.2 Risk-Aware Design in Structural and Civil Engineering 61.5 From Reliability to Resilience Paradigm 71.5.1 Key Differentiators Between Reliability and Resilience 71.5.2 Expanding Resilience Practices 81.5.2.1 Broadening the Scope of Contingencies 81.5.2.2 Focusing on High-Risk Scenarios 81.5.2.3 Incorporating Environmental Interactions 81.5.2.4 Tailoring Strategies to Natural Threats 81.5.2.5 Integrating Diverse Measures and Technologies 91.5.2.6 Emphasizing Dynamics and Recovery 91.6 Fundamentals of Power System Resilience 91.6.1 Contribution to the Field 101.6.2 Closing Remarks 10References 112 Conceptualizing and Contextualizing Power Grid Resilience 132.1 Shocks and Stresses on Critical Power Infrastructure 132.2 Defining Power System Resilience 152.3 Resilience Capacities and Features 182.4 Comparing and Clarifying Reliability and Resilience 202.5 Conceptualizing Power System Resilience to External Shocks 222.6 Domains of Resilience 262.6.1 Infrastructure Resilience 262.6.2 Operational Resilience 272.6.3 Organizational Resilience 272.6.4 Community Resilience 27References 283 System Resilience Assessment and Quantification 313.1 Needed Resilience Metrics for Power Systems 313.2 Quantifying the Resilience Trapezoid 323.2.1 The FLEP and Area Metric Systems 323.2.2 Fragility-Driven Resilience Assessment Against Windstorms 353.3 CVaR-Driven Resilience Assessment 433.3.1 Illustrative Example of CVaR Resilience Assessment Against Wind Events 443.4 AC Cascading Modeling for Resilience Applications 453.4.1 Recursive Application of Protection Mechanisms 483.4.2 Obtaining a Solvable PF 503.4.3 Implementation of Protection Mechanisms 503.4.3.1 Cascade Visualization 543.4.4 Integration into Resilience Metric Frameworks 54References 584 Addressing Data Granularity and Ambiguity 614.1 Understanding Outage Models on Power Systems 614.2 Homogeneous Versus Distributed Representations of Failure Hazard on Overhead Lines 664.2.1 Homogeneous Representations of Outage Risk on Lines 674.3 Distributed Failure Risk Representation on Lines 674.4 Method for Representing Spatial Risk of a Natural Hazard 704.5 Data Acquisition 704.5.1 Calculating Exposure of System to Natural Hazards 714.5.2 Modeling Failure Probability 734.5.3 Correcting Wind Speed Data for Different Heights of Asset 764.5.4 Interpolation of Datasets for the Purposes of Resilience Studies 774.5.5 A Tractable Method for Calculating Wind Power Outputs in Extreme Wind Events 784.5.6 A Case Study Using Demonstrated Methods on the Northern Scottish Transmission System 794.6 Exercises 844.7 Correlated Natural Hazards 864.8 Incorporating Imprecise Fragility Curves in Decision-Making Models 904.9 Summary 91Acknowledgments 92Reference 925 Resilient Investment Planning 955.1 Network Investment Decisions: Unraveling the Planner’s Trilemma 955.1.1 Expanding and Hardening Solutions 955.1.2 Digitalized, Non-Wire and Smart Grid Solutions 965.1.3 The Resilience Enhancement Trilemma 975.2 Resilience and Risk Metrics for Risk-Averse Decision-Making 985.2.1 A Probabilistic Risk Metric 1005.2.2 Risk Versus Resilience Metrics 1015.2.3 Dependencies and Common Mode 1015.2.4 Example of Probability Capacity Tables Accounting for Dependencies in a Double Circuit 1025.2.5 Deterministic or “Robust” Approach to Risk 1035.2.6 Distributionally Robust Approach to Risk 1045.3 Mathematical Frameworks to Plan Resilient Grids 1045.3.1 Possible Theoretical Formulations: From Robust to Stochastic Network Planning 1045.3.1.1 Two-Stage Framework 1045.3.1.2 Multi-Stage Framework with Two Layers of Uncertainty 1055.3.2 CVaR Formulation 1065.3.3 Optimization via Simulation Approach: A Two-Stage Stochastic Model 1065.3.4 Advanced Resilient Investment Planning Models 1095.4 Merging Resilience and Reliability Criteria for Practical Decisions 1105.4.1 Illustrative Case Study 1105.4.2 Reliability I: Adequacy 1105.4.3 Reliability II: Security 1105.4.4 Resilience 1115.4.5 Combining Reliability and Resilience 1135.5 Realistic Application to Earthquakes in Chile 1135.5.1 Case Study Description 1145.5.2 Results: Portfolio Solutions for Resilience Enhancement 1155.6 Main Grid Resilience Investments Versus DER 1165.6.1 A Suitable Methodology to Design DER Portfolios Against Wildfires 1165.6.2 Illustrative Case Study Example 1185.6.3 The Classic N–1 Design 1195.6.4 The Resilient Design 1205.6.5 The Actual Risks Associated with the Current Security Standards 1205.7 Investment Versus Operational Measures 1215.7.1 A Comment on Resilience and CVaR Effects on Portfolio Diversification 1225.8 Fairness Considerations in Resilience 1225.9 Beyond Networks: Long-Term Duration Energy Storage to Enhance Future Energy System Resilience Against Prolonged Low Output of RES 124References 1276 Operational Resilience Planning 131Nomenclature 1316.1 Introduction 1326.2 Smart Operational Measures 1356.3 Preventive Unit Commitment to Enhance Power System Resilience Under Extreme Weather Events 1366.3.1 Resilience Preventive Unit Commitment Using Robust Optimization 1386.3.1.1 Mathematical Formulation 1386.3.1.2 Problem Reformulation and Solution Algorithm 1406.3.1.3 Case Study Applications 1416.3.2 Machine Learning Techniques to Deal with Multiple Line Failures Under Extreme Events 1456.3.2.1 Mathematical Formulation 1456.3.2.2 Machine Learning Assisted Stochastic Unit Commitment 1476.3.2.3 Case Study Applications 1486.4 Defensive Islanding to Enhance Power System Resilience Under Extreme Weather Events 1516.4.1 Defensive Islanding Algorithm 1516.4.2 Approach for Determining when to Apply Defensive Islanding 1536.4.3 Case Study Applications 1546.5 Resilience Enhancement in Low-Carbon, Low-Inertia Power Systems 1606.5.1 Dynamic Network Model 1616.5.2 Mathematical Formulation 1626.5.3 Case Study Applications 1636.5.3.1 Base Case Results 1646.5.3.2 SECOPF Results 1656.6 Appendix 1676.6.1 Reformulation and Solution Algorithm of Tri-level Problems 1676.6.2 Solution Algorithm 168References 1687 Resilience by Distributed Energy Resources and Microgrids 1777.1 Local and Bulk System Resilience 1777.1.1 Overview of Microgrids 1787.1.2 Resilient Decarbonization of Multi-Energy Microgrids 1797.1.3 Electrified Transport Sector and Mobile Sources Enhancing Resilience 1817.2 Resilience Support by Real-World Microgrids 1817.2.1 Princeton Microgrid Against Hurricanes – United States 1817.2.2 The Sendai Microgrid During and After the Tsunami and Large-Scale Earthquake – Japan 1827.2.3 Blue Lake Rancheria Microgrid Against Wildfires – United States 1827.2.4 Texas Microgrids Against Winter Storms – United States 1837.2.5 Louisiana Microgrids Against Hurricanes – United States 1847.2.6 Microgrids Against Earthquakes – Haiti 1857.2.7 The Kythnos Microgrid During Natural Disasters – Greece 1857.2.8 Support from Mobile Generators – Ad Hoc Microgrids Against Wildfires – Greece 1867.2.9 Support from Local Generation Islanded Operation of Constitución Against Wildfires – Chile 1867.3 DER/Microgrids Role in Strengthening Resilience 1877.3.1 Resilience Enhancement at All Power System Levels 1877.3.2 Resilience Enhancement in All Resilience Phases 1877.4 Preventive and Corrective Microgrid Formation 1897.4.1 The Base Model 1897.4.1.1 Partitioning Constraints 1907.4.1.2 Operating Constraints 1947.4.1.3 Objective Function 1947.4.1.4 Numerical Results 1957.4.2 Advances of the Base Model 1977.4.2.1 Reformulating the Partitioning Constraints 1977.4.2.2 Further Advances in MGs Formulation 1997.4.2.3 Integration with DER Scheduling 2007.5 Microgrids for Resilience-Oriented Restoration 2017.5.1 Microgrids Aided Distribution System Restoration 2017.5.1.1 Operating Constraints 2027.5.1.2 Connectivity and Sequence Constraints 2037.5.1.3 Topological Constraints 2047.5.1.4 Initial Condition Constraints 2047.5.1.5 Optimization Formulation 2047.5.2 Restoration of a Microgrid 2057.5.2.1 Microgrid Restoration Sequence 2057.5.2.2 Protection Considerations 2067.5.2.3 Decentralized Techniques 2067.6 Resilience-Oriented Preventive and Emergency DER Scheduling 2077.6.1 Problem Formulation 2077.6.2 Study Case Application 2097.6.2.1 Test Network and Simulation Data 2097.6.2.2 Operation Against Approaching Wildfire 211References 2158 Resilience of Low-Carbon Power Systems: Standards, Market, Regulatory, and Policy Aspects 2218.1 Introduction 2218.2 Weather and Low-Carbon Grid Reliability 2218.3 Weather and Low-Carbon Grid Resilience 2228.4 From Reliability to Resilience in Low-Carbon Grids: Need for New Security Standards 2238.5 Toward a New Regulatory Framework for Resilience 2258.6 Measuring Power System Resilience 2278.7 The Economics of Resilience: “Value of Customer Resilience” and Risk Aversion 2298.8 The Economics of Resilience: Cost–Benefit Analysis and Risk Aversion 2328.9 The Economics of Resilience: Cost-Effectiveness Analysis 2328.10 Regulation, Policy, and Markets: Who Should Provide Resilience? 2338.11 Regulation, Policy and Markets: Who Should Pay for Resilience? 2358.12 Resilience, Decarbonization Policies, and Digitalization Paradigm 2358.13 A Regulatory Perspective on Resilience: Final Considerations 237References 238Index 241