Predictability and Fairness in Load Aggregation and Operations of Virtual Power Plants

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 suggest 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. We show that 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.