One of the widely used peak reduction methods in smart grids is demand response, where one analyzes the shift in customers' (agents') usage patterns in response to the signal from the distribution company. Often, these signals are in the form of incentives offered to agents. This work studies the effect of incentives on the probabilities of accepting such offers in a real-world smart grid simulator, PowerTAC. We first show that there exists a function that depicts the probability of an agent reducing its load as a function of the discounts offered to them. We call it reduction probability (RP). RP function is further parametrized by the rate of reduction (RR), which can differ for each agent. We provide an optimal algorithm, MJS--ExpResponse, that outputs the discounts to each agent by maximizing the expected reduction under a budget constraint. When RRs are unknown, we propose a Multi-Armed Bandit (MAB) based online algorithm, namely MJSUCB--ExpResponse, to learn RRs. Experimentally we show that it exhibits sublinear regret. Finally, we showcase the efficacy of the proposed algorithm in mitigating demand peaks in a real-world smart grid system using the PowerTAC simulator as a test bed.

翻译：智能电网中广泛使用的尖峰削减方法之一是需求响应，该方法通过分析用户（智能体）对配电公司信号响应的用电模式变化来实现。通常，这类信号以向智能体提供激励的形式呈现。本研究在真实世界的智能电网模拟器PowerTAC中，探讨了激励对智能体接受此类报价概率的影响。我们首先证明存在一个函数，能够描述智能体负荷削减概率随所提供折扣变化的关系，并将其称为削减概率（RP）。RP函数进一步由削减速率（RR）参数化，而RR值可能因智能体而异。我们提出了一种最优算法MJS—ExpResponse，该算法在预算约束下通过最大化期望削减量，输出分配给每个智能体的折扣值。当RR未知时，我们提出了一种基于多臂老虎机（MAB）的在线算法（即MJSUCB—ExpResponse）来学习RR值。实验证明，该算法具有次线性遗憾值。最后，我们以PowerTAC模拟器为实验平台，展示了所提算法在实际智能电网系统中缓解尖峰负荷的有效性。