In power systems, one wishes to regulate the aggregate demand of an ensemble of distributed energy resources (DERs), such as controllable loads and battery energy storage systems. We propose a notion of predictability and fairness, which suggests that the long-term averages of prices or incentives offered should be independent of the initial states of the operators of the DER, the aggregator, and the power grid. We show that this notion cannot be guaranteed with many traditional controllers used by the load aggregator, including the usual proportional–integral (PI) controller. However, even considering the non-linearity of the alternating-current model, this notion of predictability and fairness can be guaranteed for incrementally input-to-state stable (iISS) controllers, under mild assumptions.

在电力系统中，人们希望调节一组分布式能源 (DER) 的总需求，例如可控负载和电池储能系统。我们提出了可预测性和公平性的概念，这表明价格的长期平均值或提供的激励措施应该独立于 DER、聚合器和电网的运营商的初始状态。我们表明，负载聚合器使用的许多传统控制器无法保证这一概念，包括通常的比例积分 (PI) 控制器。然而，即使考虑到交流电模型的非线性，在温和的假设下，对于增量输入状态稳定 (iISS) 控制器，这种可预测性和公平性的概念也可以得到保证。