Control and Optimization Methods for Complex System Resilience

Preface
Acknowledgements
Contents
Acronyms
Nomenclature
1 Introduction to Complex System Resilience
	1.1 Background
	1.2 Literature Review
		1.2.1 Risk Identification
		1.2.2 System Protection
		1.2.3 System Recovery
	1.3 Outline of the Book
	References
2 Optimal Control Approach to Identifying Cascading Failures
	2.1 Introduction
	2.2 Problem Formulation
		2.2.1 Cascading Model
		2.2.2 DC Power Flow Equation
		2.2.3 Optimization Formulation
	2.3 Theoretical Analysis
	2.4 Simulation and Validation
		2.4.1 Numerical Simulations
		2.4.2 Cascading Validation
		2.4.3 Scalability
	2.5 Conclusions
	2.6  Appendix
		2.6.1  Proof of Lemma 2.1
		2.6.2  Proof of Lemma 2.2
		2.6.3  Proof of Lemma 2.3
		2.6.4  Proof of Theorem 2.1
	References
3 Jacobian-Free Newton-Krylov Method for Risk Identification
	3.1 Introduction
	3.2 Problem Formulation
		3.2.1 Cascading Failure Process
		3.2.2 Mathematical Model
		3.2.3 Optimization Formulation
	3.3 Numeric Solver
	3.4 Case Study
		3.4.1 Cascade Model
		3.4.2 Parameter Setting
		3.4.3 Simulation and Validation
		3.4.4 Statistical Analysis
		3.4.5 Applicability
	3.5 Conclusions
	3.6  Appendix
		3.6.1  FACTS Devices
		3.6.2  HVDC Links
		3.6.3  Protective Relay
	References
4 Security Monitoring Using Converse Lyapunov Function
	4.1 Introduction
	4.2 ROA of General Dynamical Systems
	4.3 GP for Learning Unknown Dynamics
		4.3.1 Gaussian Process and RKHS Norm
		4.3.2 GP-UCB Based Algorithm
	4.4 Main Results
	4.5 Numerical Simulations
		4.5.1 Power System Model
		4.5.2 SMIB System
		4.5.3 IEEE 39 Bus System
		4.5.4 Discussions
	4.6 Conclusions and Future Work
	4.7  Appendix
		4.7.1  The Class Γ Function
		4.7.2  Upper Bound of Discretizing Error
		4.7.3  Information Gain
		4.7.4  Computation of RKHS Norm
		4.7.5  Proof of Theorem 4.2
	References
5 Online Gaussian Process Learning for Security Assessment
	5.1 Introduction
	5.2 The ROA of DAE System
	5.3 The Windowed Online GP
		5.3.1 GP Regression
		5.3.2 Windowed Online GP
	5.4 Security Assessment Scheme
	5.5 Case Study
		5.5.1 Validations with PMU Data
		5.5.2 Discussions
	5.6 Conclusions and Future Work
	5.7  Appendix
		5.7.1  Proof of Theorem 5.1
		5.7.2  The Operator R
		5.7.3  Proof of Theorem 5.2
	References
6 Risk Identification of Cascading Process Under Protection
	6.1 Introduction
	6.2 Problem Formulation
		6.2.1 State Equation
		6.2.2 Protective Actions
		6.2.3 Cost Function
	6.3 Theoretical Results
	6.4 Simulation and Validation
		6.4.1 Parameter Setting
		6.4.2 Validation and Comparison
	6.5 Conclusions
	References
7 Model Predictive Approach to Preventing Cascading Proces
	7.1 Introduction
	7.2 Protection Architecture
	7.3 Nonrecurring Protection Scheme
	7.4 Recurring Protection Scheme
	7.5 Numerical Simulations
		7.5.1 Parameter Setting
		7.5.2 Validation and Comparison
		7.5.3 Effect of Tuning Parameters
		7.5.4 Other Test Systems
	7.6 Discussions
	7.7 Conclusions
	7.8  Appendix
		7.8.1  Definition of Operators
		7.8.2  Proof of Equation7.2
		7.8.3  Proof of Proposition 7.3.3
	References
8 Robust Optimization Approach to Uncertain Cascading Process
	8.1 Introduction
	8.2 Prediction of Cascading Failure Paths
		8.2.1 Markov Chain Model
		8.2.2 Dimensionality Reduction
	8.3 Robust Optimization Formulation
	8.4 Numerical Solver Using Dykstra\'s Algorithm
	8.5 Simulation and Validation
		8.5.1 Parameter Setting
		8.5.2 Validation and Discussion
	8.6 Conclusions
	References
9 Cooperative Control Methods for Relieving System Stress
	9.1 Introduction
	9.2 Problem Formulation
	9.3 Coordination Controller
		9.3.1 Generation of Control Signals
		9.3.2 Construction of Jacobian Estimator
	9.4 Numerical Simulations
	9.5 Conclusions
	9.6  Appendix
	References
10 Distributed Optimization Approach to System Protection
	10.1 Introduction
	10.2 Preliminaries
		10.2.1 Hybrid Model
		10.2.2 Communication Topology
	10.3 Problem Formulation
	10.4 Control Design and Theoretical Analysis
		10.4.1 Control Law of TCPST
		10.4.2 Distributed Optimization Algorithm
		10.4.3 Convergence Analysis
	10.5 Numerical Simulations
		10.5.1 Reduction of Branch Capacity
		10.5.2 Bus Overloads
		10.5.3 Effect of Tuning Parameters
	10.6 Conclusions
	References
11 Reinforcement Learning Approach to System Recovery
	11.1 Introduction
	11.2 Problem Formulation
	11.3 Restoration Scheme
	11.4 Numerical Results
		11.4.1 Static Load
		11.4.2 Dynamic Load
	11.5 Conclusion
	References
12 Summary and Future Work
	12.1 Summary of the Book
	12.2 Future Directions
	References