YINLIANG XU, PHD, is now an Associate Professor with Tsinghua-Berkeley Shenzhen Institute, Tsinghua Shenzhen International Graduate School, Tsinghua University, P. R. China. WEI ZHANG, PHD, is a Postdoc Resercher Associate with Department of Civil, Environmental, and Construction Engineering of College of Engineering & Computer Science, University of Central Florida, Orlando, Florida, USA. WENXIN LIU, PHD, is an Associate Professor with the Department of Electrical and Computer Engineering, Lehigh University, Bethlehem, PA, USA. WEN YU, PHD, is a Professor with the Departamento de Control Automatico with the Centro de Investigación y de Estudios Avanzados, Instituto Politécnico Nacional (CINVESTAV-IPN), Mexico City, Mexico.

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• About the Authors xiiiPreface xvAcknowledgment xixList of Figures xxiList of Tables xxxi1 Background 11.1 Power Management 11.2 Traditional Centralized vs. Distributed Solutions to Power Management 41.3 Existing Distributed Control Approaches 52 Algorithm Evaluation 92.1 Communication Network Topology Configuration 92.1.1 Communication Network Design for Distributed Applications 92.1.2 N −1 Rule for Communication Network Design 112.1.3 Convergence of Distributed Algorithms with Variant Communication Network Typologies 132.2 Real-Time Digital Simulation 162.2.1 Develop MAS Platform Using JADE 162.2.2 Test-Distributed Algorithms Using MAS 182.2.2.1 Three-Agent System on the Same Platform 182.2.2.2 Two-Agent System with Different Platforms 192.2.3 MAS-Based Real-Time Simulation Platform 20References 223 Distributed Active Power Control 233.1 Subgradient-Based Active Power Sharing 233.1.1 Introduction 243.1.2 Preliminaries - Conventional Droop Control Approach 263.1.3 Proposed Subgradient-Based Control Approach 273.1.3.1 Introduction of Utilization Level-Based Coordination 273.1.3.2 Fully Distributed Subgradient-Based Generation Coordination Algorithm 283.1.3.3 Application of the Proposed Algorithm 313.1.4 Control of Multiple Distributed Generators 333.1.4.1 DFIG Control Approach 333.1.4.2 Converter Control Approach 343.1.4.3 Pitch Angle Control Approach 353.1.4.4 PV Generation Control Approach 363.1.4.5 Synchronous Generator Control Approach 363.1.5 Simulation Analyses 373.1.5.1 Case 1 – Constant Maximum Available Renewable Generation and Load 383.1.5.2 Case 2 – Variable Maximum Available Renewable Generation and Load 413.1.6 Conclusion 453.2 Distributed Dynamic Programming-Based Approach for Economic Dispatch in Smart Grids 463.2.1 Introduction 463.2.2 Preliminary 493.2.3 Graph Theory 493.2.4 Dynamic Programming 493.2.5 Problem Formulation 493.2.6 Economic Dispatch Problem 503.2.7 Discrete Economic Dispatch Problem 503.2.8 Proposed Distributed Dynamic Programming Algorithm 513.2.9 Distributed Dynamic Programming Algorithm 523.2.10 Algorithm Implementation 533.2.11 Simulation Studies 543.2.12 Four-generator System: Synchronous Iteration 543.2.12.1 Minimum Generation Adjustment Δpi = 2.5MW 543.2.12.2 Minimum Generation Adjustment Δpi = 1.25MW 573.2.13 Four-Generator System: Asynchronous Iteration 593.2.13.1 Missing Communication with Probability 593.2.13.2 Gossip Communication 603.2.14 IEEE 162-Bus System 613.2.15 Hardware Implementation 633.2.16 Conclusion 643.3 Constrained Distributed Optimal Active Power Dispatch 653.3.1 Introduction 653.3.2 Problem Formulation 673.3.3 Distributed Gradient Algorithm 683.3.4 Distributed Gradient Algorithm 683.3.5 Inequality Constraint Handling 703.3.6 Numerical Example 723.3.6.1 Case 1 723.3.6.2 Case 2 743.3.7 Control Implementation 753.3.8 Communication Network Design 763.3.9 Generator Control Implementation 763.3.10 Simulation Studies 773.3.11 Real-Time Simulation Platform 783.3.12 IEEE 30-Bus System 783.3.12.1 Constant Loading Conditions 803.3.12.2 Variable Loading Conditions 823.3.12.3 With Communication Channel Loss 843.3.13 Conclusion and Discussion 863.A Appendix 86References 874 Distributed Reactive Power Control 974.1 Q-Learning-Based Reactive Power Control 974.1.1 Introduction 984.1.2 Background 994.1.3 Algorithm Used to Collect Global Information 994.1.4 Reinforcement Learning 1014.1.5 MAS-Based RL Algorithm for ORPD 1014.1.6 RL Reward Function Definition 1024.1.7 Distributed Q-Learning for ORPD 1034.1.8 MASRL Implementation for ORPD 1044.1.9 Simulation Results 1064.1.10 Ward–Hale 6-Bus System 1064.1.10.1 Learning from Scratch 1084.1.10.2 Experience-Based Learning 1104.1.10.3 IEEE 30-Bus System 1124.1.10.4 IEEE 162-Bus System 1144.1.11 Conclusion 1154.2 Sub-gradient-Based Reactive Power Control 1164.2.1 Introduction 1164.2.2 Problem Formulation 1194.2.3 Distributed Sub-gradient Algorithm 1204.2.4 Sub-gradient Distribution Calculation 1224.2.4.1 Calculation of 𝜕f ∕𝜕Qci for Capacitor Banks 1224.2.4.2 Calculation of 𝜕f ∕𝜕Vgi for a Generator 1244.2.4.3 Calculation of 𝜕f ∕𝜕tti for a Transformer 1244.2.5 Realization of Mas-Based Solution 1264.2.5.1 Computation of Voltage Phase Angle Difference 1274.2.5.2 Generation Control for ORPC 1284.2.6 Simulation and Tests 1294.2.6.1 Test of the 6-BusWard–Hale System 1294.2.6.2 Test of IEEE 30-Bus System 1344.2.7 Conclusion 141References 1415 Distributed Demand-Side Management 1475.1 Distributed Dynamic Programming-Based Solution for Load Management in Smart Grids 1485.1.1 System Description and Problem Formulation 1505.1.2 Problem Formulation 1515.1.3 Distributed Dynamic Programming 1535.1.3.1 Abstract Framework of Dynamic Programming (DP) 1535.1.3.2 Distributed Solution for Dynamic Programming Problem 1545.1.4 Numerical Example 1575.1.5 Implementation of the LM System 1585.1.6 Simulation Studies 1605.1.6.1 Test with IEEE 14-bus System 1605.1.6.2 Large Test Systems 1665.1.6.3 Variable Renewable Generation 1685.1.6.4 With Time Delay/Packet Loss 1705.1.7 Conclusion and Discussion 1715.2 Optimal Distributed Charging Rate Control of Plug-in Electric Vehicles for Demand Management 1725.2.1 Background 1755.2.2 Problem Formulation of the Proposed Control Strategy 1755.2.3 Proposed Cooperative Control Algorithm 1805.2.3.1 MAS Framework 1805.2.3.2 Design and Analysis of Distributed Algorithm 1805.2.3.3 Algorithm Implementation 1815.2.3.4 Simulation Studies 1835.3 Conclusion 190References 1916 Distributed Social Welfare Optimization 1976.1 Introduction 1976.2 Formulation of OEM Problem 2006.2.1 SocialWelfare Maximization Model 2006.2.2 Market-Based Self-interest Motivation Model 2036.2.3 Relationship Between Two Models 2046.3 Fully Distributed MAS-Based OEM Solution 2076.3.1 Distributed Price Updating Algorithm 2076.3.2 Distributed Supply–Demand Mismatch Discovery Algorithm 2096.3.3 Implementation of MAS-Based OEM Solution 2106.4 Simulation Studies 2126.4.1 Tests with a 6-bus System 2126.4.1.1 Test Under the Constant Renewable Generation 2146.4.1.2 Test Under Variable Renewable Generation 2176.4.2 Test with IEEE 30-bus System 2186.5 Conclusion 221References 2217 Distributed State Estimation 2257.1 Distributed Approach for Multi-area State Estimation Based on Consensus Algorithm 2257.1.1 Problem Formulation of Multi-area Power System State Estimation 2277.1.2 Distributed State Estimation Algorithm 2287.1.3 Approximate Static State Estimation Model 2317.1.4 Regarding Implementation of Distributed State Estimation 2337.1.5 Case Studies 2347.1.5.1 With the Accurate Model 2357.1.5.2 Comparisons Between Accurate Model and Approximate Model 2387.1.5.3 With Variable Loading Conditions 2397.1.6 Conclusion and Discussion 2417.2 Multi-agent System-Based Integrated Solution for Topology Identification and State Estimation 2427.2.1 Measurement Model of the Multi-area Power System 2447.2.2 Distributed Subgradient Algorithm for MAS-Based Optimization 2457.2.3 Distributed Topology Identification 2487.2.3.1 Measurement Modeling 2487.2.3.2 Distributed Topology Identification 2517.2.3.3 Statistical Test for Topology Error Identification 2527.2.4 Distributed State Estimation 2537.2.5 Implementation of the Integrated MAS-Based Solution for TI and SE 2547.2.6 Simulation Studies 2557.2.6.1 IEEE 14-bus System 2557.2.6.2 Large Test Systems 2637.3 Conclusion and Discussion 266References 2678 Hardware-Based Algorithms Evaluation 2718.1 Steps of Algorithm Evaluation 2718.2 Controller Hardware-In-the-Loop Simulation 2738.2.1 PC-Based C-HIL Simulation 2748.2.2 DSP-Based C-HIL Simulation 2778.3 Power Hardware-In-the-Loop Simulation 2798.4 Hardware Experimentation 2818.4.1 Test-bed Development 2818.4.2 Algorithm Implementation 2848.5 Future Work 2889 Discussion and Future Work 291References 296Index 297