This book provides a systematic framework to enhance the ability of complex dynamical systems in risk identification, security assessment, system protection, and recovery with the assistance of advanced control and optimization technologies. By treating external disturbances as control inputs, optimal control approach is employed to identify disruptive disturbances, and online security assessment is conducted with Gaussian process and converse Lyapunov function. Model predictive approach and distributed optimization strategy are adopted to protect the complex system against critical contingencies. Moreover, the reinforcement learning method ensures the efficient restoration of complex systems from severe disruptions. This book is meant to be read and studied by researchers and graduates. It offers unique insights and practical methodology into designing and analyzing complex dynamical systems for resilience elevation.
Author(s): Chao Zhai
Series: Studies in Systems, Decision and Control, 478
Publisher: Springer
Year: 2023
Language: English
Pages: 217
City: Singapore
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
