# Predictability and Fairness in Load Aggregation with Deadband

arXiv: https://arxiv.org/abs/2305.17725 · HTML: https://mlsanity.com/paper/2305.17725/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 32 references that are in the map.
- First posted on arXiv 28 May 2023.

## Builds on (most cited first, 6 of 6)

- [On the Ergodic Control of Ensembles](https://mlsanity.com/paper/1807.03256/) (2018)
- [Predictability and Fairness in Load Aggregation and Operations of Virtual Power Plants](https://mlsanity.com/paper/2110.03001/) (2021)
- [Real-time Flexibility Feedback for Closed-loop Aggregator and System Operator Coordination](https://mlsanity.com/paper/2006.13814/) (2020)
- [A distributed scheme for secondary frequency control with stability guarantees and optimal power allocation](https://mlsanity.com/paper/1806.11449/) (2018)
- [Time-varying Projected Dynamical Systems with Applications to Feedback Optimization of Power Systems](https://mlsanity.com/paper/1809.07288/) (2018)
- [Primary frequency regulation in power grids with on-off loads: chattering, limit cycles and convergence to optimality](https://mlsanity.com/paper/1908.08077/) (2019)

## Abstract (arXiv)

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.