本論文探討智慧電網的分散式需求響應問題，以達到電力供需平衡及調節供電頻率。在現存的分散式負載控制方法中，每個使用者通常需要互相通訊，進行交換訊息，最近的研究結果表明基於供電頻率的相關估測能達成全分散式的負載控制。然而現存的方法中限制了最佳化的目標式需要為強凸並且連續二次可微的函數。基於更廣泛的應用，本篇論文提出一個基於交替方向乘子法（proximalJacobi Alternating Direction Multipliers Method, ADMM）的負載控制演算法。此全分散式演算法可應用於目標式為任意凸函數，此外，本論文更延伸此方法至異步設置(asynchronous setup)。異步演算法可以分散負載避免其過度的同步更新,故其特性相當適用於負載數量很大的情況。模擬結果證明了我們提出的演算法即使在有雜訊干擾的情況，同步及異步演算法皆可以有效的達到頻率穩定的效果。

In this paper, we consider a distributed load control problem for achieving supply-demand balance and frequency regulation in a power system. While most of the distributed load control schemes require the loads to exchange in- formation through two-way communications, recent results have shown that it is possible to achieve fully distributed control by frequency-based imbalance estimation. However, the existing methods need the load disutility functions or the sum of them to be strongly convex. For a wider range of application scenarios, we propose a new load control algorithm based on the proximal Ja- cobi alternating direction method of multipliers (PJ-ADMM). The proposed algorithm works for arbitrary convex disutility functions. Moreover, we ex- tend the PJ-ADMM based load control algorithm to an asynchronous setup.
Asynchronous updates can spare the loads from strict synchronization and are particularly useful when the number of loads is large. Simulation results are presented to show that the proposed algorithms regulate the frequency to the nominal value well, in both synchronous and asynchronous scenarios and with and without imbalance estimation errors.

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