Cover
Title Page
Copyright
Contents
Foreword
Preface
Acknowledgments
Chapter 1 Introduction
1.1 Traditional Hierarchical Control Structure
1.1.1 Hierarchical Frequency Control
1.1.1.1 Primary Frequency Control
1.1.1.2 Secondary Frequency Control
1.1.1.3 Tertiary Frequency Control
1.1.2 Hierarchical Voltage Control
1.1.2.1 Primary Voltage Control
1.1.2.2 Secondary Voltage Control
1.1.2.3 Tertiary Voltage Control
1.2 Transitions and Challenges
1.3 Removing Central Coordinators: Distributed Coordination
1.3.1 Distributed Control

1.3.2 Distributed Optimization
1.4 Merging Optimization and Control
1.4.1 Optimization-Guided Control
1.4.2 Feedback-Based Optimization
1.5 Overview of the Book
Bibliography
Chapter 2 Preliminaries
2.1 Norm
2.1.1 Vector Norm
2.1.2 Matrix Norm
2.2 Graph Theory
2.2.1 Basic Concepts
2.2.2 Laplacian Matrix
2.3 Convex Optimization
2.3.1 Convex Set
2.3.1.1 Basic Concepts
2.3.1.2 Cone
2.3.2 Convex Function
2.3.2.1 Basic Concepts
2.3.2.2 Jensen's Inequality
2.3.3 Convex Programming
2.3.4 Duality
2.3.5 Saddle Point
2.3.6 KKT Conditions

2.4 Projection Operator
2.4.1 Basic Concepts
2.4.2 Projection Operator
2.5 Stability Theory
2.5.1 Lyapunov Stability
2.5.2 Invariance Principle
2.5.3 Input-Output Stability
2.6 Passivity and Dissipativity Theory
2.6.1 Passivity
2.6.2 Dissipativity
2.7 Power Flow Model
2.7.1 Nonlinear Power Flow
2.7.1.1 Bus Injection Model (BIM)
2.7.1.2 Branch Flow Model (BFM)
2.7.2 Linear Power Flow
2.7.2.1 DC Power Flow
2.7.2.2 Linearized Branch Flow
2.8 Power System Dynamics
2.8.1 Synchronous Generator Model
2.8.2 Inverter Model
Bibliography

Chapter 3 Bridging Control and Optimization in Distributed Optimal Frequency Control
3.1 Background
3.1.1 Motivation
3.1.2 Summary
3.1.3 Organization
3.2 Power System Model
3.2.1 Generator Buses
3.2.2 Load Buses
3.2.3 Branch Flows
3.2.4 Dynamic Network Model
3.3 Design and Stability of Primary Frequency Control
3.3.1 Optimal Load Control
3.3.2 Main Results
3.3.3 Implications
3.4 Convergence Analysis
3.5 Case Studies
3.5.1 Test System
3.5.2 Simulation Results
3.6 Conclusion and Notes
Bibliography

Chapter 4 Physical Restrictions: Input Saturation in Secondary Frequency Control
4.1 Background
4.2 Power System Model
4.3 Control Design for Per-Node Power Balance
4.3.1 Control Goals
4.3.2 Decentralized Optimal Controller
4.3.3 Design Rationale
4.3.3.1 Primal-Dual Algorithms
4.3.3.2 Design of Controller (4.6)
4.4 Optimality and Uniqueness of Equilibrium
4.5 Stability Analysis
4.6 Case Studies
4.6.1 Test System
4.6.2 Simulation Results
4.6.2.1 Stability and Optimality
4.6.2.2 Dynamic Performance
4.6.2.3 Comparison with AGC