近年來，由於分佈式計算技術已逐漸成熟，各種新興分佈式演算法與控制法則，已逐漸應用於現代之智慧電網中。本文提出以下兩種新興之應用，包含(i)改善孤立式微電網的分佈式垂降控制方法，以及 (ii) 即時評估包含高滲透率再生能源電力系統之概率式可用輸電能力即時評估。

本文首先探討孤立微電網之分佈式垂降控制。由於微電網內再生能源之間歇性與隨機性，會造成微電網各匯流排頻率與電壓震幅之擾動。為解決此一問題，習知的作法為於再生發電源併網介面之電力轉換器內，個別實現垂降控制迴路。但此方式僅可有效控制局部之擾動。而當微電網遭受大規模之擾動時，因缺乏中央控制器，無法有效協調控制與抑制擾動。近年來，各種先進資通技術蓬勃發展，多重代理人技術也已應用於微電網控制上，達到微電網各種設備，可即插即用之目的。其中特別是共識解之轉換器垂降控制，已成為目前發展之主流。因該方法僅需透過鄰近轉換器間資訊交換，即可達成準確之垂降控制，完成電力轉換器自主式之有效功率與無效功率正確分配。然而，此控制法之收斂速度仍有待改進，且因需與其鄰近轉換器間資訊交換，通信成本仍較高。為解決此一問題，本文更進一步應用先進之牽制控制技術，於獨立微電網中之共識型分散垂降控制。此牽制控制之特色為將整體微電網分區，僅需各區之領袖代理人溝通，即可達到電網之叢集共識效果。因極少數代理人參與整體決策，因此通信架構可大幅降低，並且閉迴路系統之快速收斂動態特性，亦可藉由Lyapunov函數推導後保證。我們將建立 JADE 與即時數位模擬平台 $OPAL-RT$ 共同模擬平台，設計牽制控制之共識型分散垂降控制。並以台灣現有之微電網，使用Matlab SimPowerSystems工具箱與Java 代理程序開發框架，進行即時模擬平台之系統開發。模擬情境包含正常運轉模式、增加負載模式、加入再生能源模式、再生能源離線模式等。模擬結果驗證了本牽制控制技術，確實可應用於孤立微電網之分佈式垂降控制，完成自主式之實功與虛功分配。

其次，將探討以分散式演算法，進行包含高滲透率再生能源電力系統之概率式可用輸電能力即時評估。具體而言，我們將可用輸電能力表述為非線性之最佳電力潮流問題。 然後，利用最佳性條件分解技術之疊代分解協調法，將上述問題分解成數個子問題，各子問題可以不同處理器，分別平行計算；而各子問題間之耦合限制，以疊代法進行協調。為了估計可用輸電能力的概率密度分布函數與累積密度函數，將使用拉丁超立方體抽樣方法，評估再生能源之發電，以分佈式計算平台，計算可用輸電能力，加速蒙特卡羅法之模擬。 本演算法首先進行可用輸電能力的初步近似，並求得平均值，最佳值，與最壞值。為驗證所提出的方法的正確性，作者使用JuMP數值最佳化程式，自行開發一模擬平台。並已IEEE 118匯流排系統，設計各種電力系統運轉情境，進行廣泛的數值模擬。模擬結果說明本方法之可行性與正確性。

In recent years, due to the enormous enhancements in distributed computing systems, the application of distributed algorithms for control and optimization of Microgrids and large-scale power grids has been proposed. In particular, various consensus-based control strategies have been integrated into Microgrid controllers aiming to improve their dynamic performance and provide accurate active and reactive power sharing among interface converters. Similarly, several distributed optimization techniques have been implemented and tested for real-time assessment and monitoring in power transmission systems. In this sense, this thesis explores innovative distributed strategies for future power systems, including small scale generation systems as well as modernized large-scale power grids. We explore and implement two distributed techniques: i) a novel distributed control approach for enhancing the operation of isolated droop-controlled Microgrids, and ii) a robust distributed optimization algorithm applied to probabilistic available transfer capability assessment of power systems with penetration of renewable energy.

First, we focus on distributed control strategies for droop-controlled Microgrids and introduce a novel approach: distributed pinning droop control. The proposed approach seeks to enhance the overall operation of the Microgrid by providing accurate active and reactive power sharing among parallel power converters. The distributed pinning droop control technique can be considered as a special leader-following consensus algorithm integrated into the traditional droop control--- used as a distributed methodology for accurate active and reactive power sharing in isolated converter-fed Microgrids. Under this proposed framework, both power converters and loads in the Microgrid are treated as intelligent agents with communication capabilities inside a multi-agent system. A great advantage of this proposed framework is that, since only a fraction of the agents in the network have access to the control reference, the required communication bandwidth and control cost can be significantly reduced without degrading the dynamical performance compared to previously proposed consensus-based droop control techniques. The proposed distributed pinning droop control mechanism is studied in a rigorous theoretical and experimental manner, including convergence criteria, the appropriate selection of the leader agents given arbitrary communication topologies and the implementation using standard multi-agent programming environments. In order to validate the correctness and applicability of the distributed pinning droop control framework, a multi-agent platform is developed for a test-bed Microgrid with multiple interface converters and loads. The test-bed system is located in northern Taiwan and the simulation results are conducted using a precise dynamical model of the system, including actual parameters of transmission lines, converter capacity and load requirements. Extensive numerical simulations under various operating conditions, including normal operations, heavy loading conditions, and plug-in and plug-out scenarios, are investigated using the SimPowerSystems toolbox and the Java Agent Development Framework.

Second, we investigate distributed optimization algorithms and their application to on-line monitoring of Available Transfer Capability in transmission systems. In particular, we explore the Optimality Conditions Decomposition algorithm for probabilistic Available Transfer Capability assessment in power systems with penetration of intermittent wind power generation. First, the Available Transfer Capability assessment is mathematically formulated as a non-linear optimal power flow problem. Then, an iterative decomposition-coordination methodology based on Optimality Conditions Decomposition techniques is implemented for distributed probabilistic Available Transfer Capability assessment. In order to estimate the probability density function and empirical cumulative density function of the Available Transfer Capability, the Latin Hypercube Sampling method is utilized for obtaining samples of the integrated wind power sources. These obtained wind power samples are appended into the proposed decomposition-coordination approach in order to compute an accelerated Monte Carlo simulation of the Available Transfer Capability at the current system state. In order to provide a preliminary approximation of the range of variation of the Available Transfer Capability, three distributed algorithms to estimate the average-case, best-case, and worst-case scenarios are studied and developed. The correctness and applicability of the proposed approach are evaluated by conducting extensive numerical simulations in the standard IEEE 118-bus system. Numerical simulations are developed using JuMP --- a Julia-based modeling language for mathematical optimization. Various operating conditions of the test-bed system are used in order to investigate the robustness of the proposed distributed probabilistic Available Transfer Capability assessment.

List of figures ix
List of tables xi
Nomenclature xiii
1 Introduction 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Distributed Control Approaches for Converter-fed Microgrids . . . . . 1
1.1.2 Distributed Optimization for ATC Assessment in Power Systems . . . . 3
1.2 Contributions of The Dissertation . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Distributed Pinning Droop Control of Isolated Microgrids 9
2.1 PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Graph Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Distributed Pinning Control . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Power Sharing in Isolated AC Microgrids . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Model Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 P-f and Q-˙V Droop Control . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Proposed Pinning Based Droop Control . . . . . . . . . . . . . . . . . . . . . 15
2.3.1 MAS development . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 Pinning Localization and Grid Partition . . . . . . . . . . . . . . . . . 15
2.3.3 Pinning-Based Droop Control . . . . . . . . . . . . . . . . . . . . . . 19
2.3.4 Stability Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Simulation Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
viii Table of contents
2.4.1 Test Bed Descriptions and Partition . . . . . . . . . . . . . . . . . . . 23
2.4.2 System Development and Testing . . . . . . . . . . . . . . . . . . . . 25
2.4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.4 Possible Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Distributed ATC Assessment in Power Systems with Variable Wind Power Generation
33
3.1 Probabilistic Model of Wind Farms . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.1 Latin Hypercube Sampling . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 ATC Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.1 ATC Assessment by the OPF formulation . . . . . . . . . . . . . . . . 36
3.2.2 Optimality Conditions Decompositions . . . . . . . . . . . . . . . . . 38
3.2.3 ATC Assessment Considering Wind Power Generation . . . . . . . . . 40
3.3 Probabilistic ATC Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 LHS-Based Monte Carlo Approach . . . . . . . . . . . . . . . . . . . 41
3.3.2 Real-Time Approximations at First Glance . . . . . . . . . . . . . . . 43
3.4 Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.1 Accuracy Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4.2 Preliminary Approximations at First Glance . . . . . . . . . . . . . . 50
3.4.3 LHS-Based Monte Carlo Approach . . . . . . . . . . . . . . . . . . . 52
4 Conclusions and Future Work 57
4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
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