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

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