近年由於分散式發電源於電網中佔比持續提升，調度各分散發電源同時維持電網電壓及頻率穩定度成為具挑戰性之課題。傳統分散式電力轉換器間之輸出協調，係透過屬於一次控制之自主垂降控制達成，此控制法之準確度受制於電網結構及傳輸線特性。於電網控制系統上建構通訊網路，於二次控制階層指揮調度發電源之實虛功輸出，將可有效解決此難題。然而，傳統之集中式二次控制需針對所有發電裝置建構高成本之集中通訊網路，且將因此不易拓展結構，與講求發電裝置可隨插即用之智慧微電網概念背道而馳。因此，本論文之目標為基於多重代理人控制理論中之共識控制法，設計新的分散式二次控制架構，以此達成分散式發電源之輸出功率
調度並強化微電網之頻率及電壓穩定度。
首先，為改善現有電力轉換器垂降控制之不足，提出一僅需稀疏通訊網路輔助之基於共識解垂降控制。有別於傳統垂降控制，所提控制法在電力網路傳輸線高度有損甚至接近純電阻情況下，依然可準確分配各發電源之實功及虛功輸出。此外，在此控制下之整體閉迴路系統穩定度，可透過非線性能量函數穩定度理論確保，故可知系統在大規模擾動下依然可維持穩定運轉。此研究亦在實時模擬環境下建置兩組微電網系統，藉此驗證所提控制於實際電網中運用之可行性。
其後，由於透過電力轉換器介面輸出之分散式發電源，不若傳統發電機組具有旋轉機械結構，在電網遭遇頻率擾動事故時，缺乏轉動慣量作為阻尼之電力轉換器將不易維持系統頻率穩定。而將同步發電機機械參數設計於電力轉換器控制架構中之虛擬同步機控制技術，將可有效解決
此問題。基於此架構下，此研究結合基於共識解之垂降控制與虛擬同步機控制技術，同時亦透過非線性能量函數穩定度框架確保整體系統之穩定度，此外亦於實時模擬環境下建構採用所提控制之微電網系統，驗證此研究於實際系統之可行性。
再者，儘管慣常之共識解控制可達成分散式發電源之輸出分配，且同時確保整體系統之穩定度，此控制之收斂速度及系統彈性大幅受制於所採用之通訊網路結構。為達成更佳之控制收斂速度及控制系統抗干擾能力，此研究採用交替方向乘子法作為二次控制階層之演算法。此演算法複雜之最佳化問題分解成子問題平行運算，在交替運算得到整體問題之最佳解，因此可大幅加快控制目標之收斂速度。此研究首先將微電網二次控制階層之控制目標以最佳化問題形式建構，接著提出兩種採用不同通訊架構之交替方向乘子法，其後確認所提控制之穩定度亦可在非線性能量函數框架獲得驗證，並於實時模擬環境下建構微電網驗證所提控制之可行性與性能。
最後，儘管於微電網二次控制階層設置網路通訊系統，可有效達成各發電源之輸出分配並強化系統之穩定度，此作法亦使控制系統暴露於網路惡意攻擊之風險下。為深入瞭解惡意攻擊對微電網系統之影響，此研究首先建構一分散式二次控制法，其後在演算法中刻意加入代表網路攻擊之擾動，推導網路通訊與物理電路間互相影響下可觀測得的狀態變化，藉此設計對應網路攻擊之偵測及隔離策略。網路攻擊模型包含只對特定通訊鏈結作擾動，以及直接竄改一運算節點之狀態兩種模型。應對策略則得利於所提之分散式演算法，可僅透過各運算節點檢查自身之運算指標達成，而不需廣泛擷取整個運算網路的狀態。最後亦將所提控制建構在實時模擬環境
下，藉以驗證其於實際微電網系統之可行性。

High penetration of distributed generation units in microgrids has led to challenges of incorporating the generation resources while maintaining the frequency and voltage stability. Traditionally, the coordination of converter-based generation is achieved by autonomous droop control, which suffers from dependence on the grid topology and power line impedances. Adopting the communication infrastructure that supports the microgrid operations, the coordinated secondary control can resolve this problem by judiciously dispatching active power resources and reactive power support. Nevertheless, the conventional centralized secondary control architecture requires high-cost communication infrastructure and is low in scalability. Due to inherently distributed and heterogeneous nature of the microgrid, it becomes an ideal platform for applications of distributed control algorithms. To this end, this dissertation aims to develop novel distributed secondary control for power converters in microgrids. The control algorithm is based on multi-agent consensus control and will be able to enhance both the real-time frequency and voltage stability.
First, the consensus-based droop control with sparse communication network is proposed to overcome the drawback of existing droop control methods. In particular, when line impedances of the power grid are either lossy with the uniform R/X ratio or even pure resistive, the consensus droop control is still an effective method for autonomous real and reactive power sharing. In addition, closed-loop system stability of the proposed consensus-based droop control method can be ensured by the energy function approach under certain mild conditions. Real-time simulations of two microgrid systems are studied to validate the feasibility of the proposed consensus-based droop control method.
Second, the conventional distributed interface converters (DICs) used in the AC microgrid have raised a major concern since they do not have a rotating mass. The almost inertia-less DIC-based microgrid configuration may result in poor frequency and voltage response during large disturbance. In order to overcome this difficulty, the virtual synchronous generator (VSGs) was proposed recently in which the DIC mimics conventional synchronous generators (SGs) by designing proper parameters of the SG into each local droop control mechanism of the DIC.
Under this framework, we deploy the distributed consensus-based control algorithm in the secondary control level of VSGs. With only neighboring information exchanged between VSGs, both the restoration of nominal operating point and the accurate generation coordination of resources can be achieved. The stability of the closed-loop system is ensured by the transient energy function under certain mild conditions. Numerical experiments of a 14-bus/6-DIC microgrid system on real-time simulators are performed to validate the effectiveness of the proposed control mechanism.
Third, although the average consensus algorithm can ensure the stability of operation points while achieving accurate power sharing among VSGs in microgrid, its convergence rate and the resilience to noises are still not satisfactory. Therefore, two implementations of consensus-based distributed droop control by the Alternating Direction Multipliers Method (ADMM) are proposed. By employing the ADMMs in the secondary control level, it can be shown that the closed-loop system is described by the second-order vector differential equation, and the stability of every trajectory can be analyzed by the energy function approach under certain mild conditions. Real-time digital simulations are performed to validate the effectiveness of the proposed distributed droop control mechanism.
Moreover, a communication-based distributed frequency control framework also exposes the microgrid assets to potential malicious cyber-attacks. To study this problem, a distributed secondary control design for isolated microgrids is first developed, and the countermeasures for malicious attacks on the communication network are then investigated. The proposed design architecture consists of the local droop control at the primary level and a distributed node-to-node update at the secondary level. The latter aims to achieve a proportional power sharing while maintaining the nominal system frequency. By casting it as a consensus optimization problem, we adopt the partial primal-dual (PPD) algorithm for a totally distributed update requiring only neighboring information exchange. Interestingly, the specially designed PPD-based control rules would mimic the network power flow dynamics. Furthermore, two types of malicious attacks on the communication network, namely, the link and node attacks, are studied. Model-based anomaly detection and localization strategies are developed based on the dual variable related metrics. Numerical simulations have been performed under a real-time simulation environment to demonstrate the effectiveness of the proposed control design and countermeasure metrics.

CHINESE ABSTRACT I
ENGLISH ABSTRACT II
ACKNOWLEDGEMENTS V
Contents VI
List of Figures XI
List of Tables XIV
Abbreviations XV
1 Introduction 1
1.1 Overview 1
1.2 Contributions of The Dissertation 6
2 Consensus-Based Droop Control Synthesis for Multiple DICs in Isolated Microgrids 9
2.1 Background 10
2.1.1 Mathematical Preliminaries 10
2.1.2 Structure-Preserving Models 12
2.1.3 Droop Control by EF Approach 13
2.2 Microgrid Droop Control in Structure-Preserving
Models 14
2.2.1 Model Descriptions 15
2.2.2 Equilibrium Analysis 16
2.2.3 Conventional Droop Control 17
2.3 Recent Droop-Control Methods 20
2.3.1 P-f and Q-Vdot Droop Control 20
2.3.2 Stability Analysis 23
2.3.3 Droop with Both f and Vdot Restorations 27
2.4 Consensus-Based Droop Control 29
2.4.1 Graph Theory and Consensus Algorithm 29
2.4.2 Operation Principles 30
2.4.3 Stability Analysis by EF 33
2.5 Real-Time Simulation Results 33
2.5.1 7-Bus Microgrid with a Single Load 35
2.5.2 14-Bus Microgrid with Multiple Loads 37
2.6 Summary 37
2.7 Appendix: Compact Forms of P-f and Q-Vdot Droop Control 40
2.8 Appendix: Compact Form for Droop with Both f and Vdot Restorations 41
3 Consensus-Based Secondary Frequency and Voltage Droop Control of Virtual
Synchronous Generators for Isolated AC Microgrids 43
3.1 Background 44
3.1.1 Average Consensus Algorithm 44
3.1.2 Virtual Synchronous Generator 45
3.2 Decentralized Local Droop Control 47
3.2.1 Model Descriptions 47
3.2.2 Control Objectives 49
3.2.3 P-f/Q-Vdot Droop Control 49
3.3 Local Droop Control with Virtual Inertia 51
3.3.1 Mechanism 51
3.3.2 Stability Analysis 52
3.4 Consensus-Based Droop Control of VSGs 54
3.4.1 Mechanism 54
3.4.2 Stability Analysis by TEF Approach 55
3.4.3 Steady-State Behaviours of Consensus-Based Droop Control 57
3.5 Real-Time Simulations 59
3.5.1 With and Without Consensus Mechanism 61
3.5.2 Damping Effects of Virtual Inertia 62
3.6 Summary 64
3.7 Appendix: Validity of TEF W(ˆy,ˆz) 67
4 Consensus-Based Droop Control of Isolated Microgrids by ADMM Implementations 70
4.1 Average Consensus Through ADMM 70
4.2 Droop Control in Isolated AC MGs 74
4.2.1 Problem Formulation 74
4.2.2 Model Descriptions 75
4.3 Consensus-Based Droop Control of VSGs 77
4.3.1 Optimal Stable Equilibrium Point 78
4.3.2 Consensus Optimization 78
4.3.3 ADMM Implementations 79
4.3.4 ADMM Implementations with Flexible Droop Gain Ratios 80
4.4 Stability Analysis of Closed-Loop MG Systems with Consensus-Based Droop Controlled VSGs 82
4.4.1 P-f/Q-Vdot Droop 83
4.4.2 ADMM Implementations 84
4.4.3 ADMM Implementations with Flexible Droop Gain Ratios 86
4.5 Real-Time Simulations 87
4.6 Summary 91
4.7 Appendix: Formulations of ˆM, ˆD, ˆA and ˆA_f 92
4.8 Appendix: Validity of EF W(ˆy,ˆz) 93
5 Frequency Control In Isolated Microgrids: Distributed Implementation And Intrusion Detection 95
5.1 System Model 96
5.1.1 P-ω Droop Control of DICs 96
5.1.2 Microgrid Network Dynamics 97
5.1.3 Equilibrium Points of Droop Controlled DICs 98
5.1.4 Consensus Optimization 99
5.2 Distributed Secondary Control Design 100
5.2.1 Update Design 100
5.2.2 Choice of Stepsize 102
5.3 Attack Models and Countermeasures 104
5.3.1 Link Attack 105
5.3.2 Node Attack 106
5.3.3 Detection/Localization Strategies 108
5.3.4 Decision Making in Energy Management System 109
5.4 Numerical Tests 111
5.4.1 Case I: Convergence Analysis 112
5.4.2 Case II: Link Attack 112
5.4.3 Case III: Node Attack 116
5.5 Summary 121
5.6 Appendix: Derivation of Update Design (5.13) 124
5.6.1 ˆf_ij-update 124
5.6.2 x-update and µ-update 124
5.7 Appendix: Convergence of Consensus Iterations (5.19) 125
6 Conclusions and Future Works 126
6.1 Conclusions 126
6.2 Future Works 129
Bibliography 131
Vita 143

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