Predictability and Fairness in Load Aggregation with Deadband
This addresses fairness and predictability issues in energy grid management, but it is incremental as it builds on prior work to handle specific non-linearities and discontinuities.
The paper tackles the problem of ensuring predictability and fairness in load aggregation for virtual power plants, where traditional regulators like PI controllers fail to guarantee long-term average prices independent of initial conditions. It demonstrates that using Filippov invariant measures allows reasoning about these properties even with non-linear AC losses and deadband discontinuities.
Virtual power plants and load aggregation are becoming increasingly common. There, one regulates the aggregate power output of an ensemble of distributed energy resources (DERs). Marecek et al. [Automatica, Volume 147, January 2023, 110743, arXiv:2110.03001] recently suggested that long-term averages of prices or incentives offered should exist and be independent of the initial states of the operators of the DER, the aggregator, and the power grid. This can be seen as predictability, which underlies fairness. Unfortunately, the existence of such averages cannot be guaranteed with many traditional regulators, including the proportional-integral (PI) regulator with or without deadband. Here, we consider the effects of losses in the alternating current model and the deadband in the controller. This yields a non-linear dynamical system (due to the non-linear losses) exhibiting discontinuities (due to the deadband). We show that Filippov invariant measures enable reasoning about predictability and fairness while considering non-linearity of the alternating-current model and deadband.