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

arXiv: https://arxiv.org/abs/2110.03001 · HTML: https://mlsanity.com/paper/2110.03001/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 88 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 11 of 11)

- [Solutions of DC OPF are Never AC Feasible](https://mlsanity.com/paper/1912.00319/) (2019)
- [Convergence Properties for Discrete-time Nonlinear Systems](https://mlsanity.com/paper/1612.05327/) (2016)
- [Adaptive Charging Networks: A Framework for Smart Electric Vehicle Charging](https://mlsanity.com/paper/2012.02636/) (2020)
- [Design and Stability of Load-Side Primary Frequency Control in Power Systems](https://mlsanity.com/paper/1305.0585/) (2013)
- [On the Ergodic Control of Ensembles](https://mlsanity.com/paper/1807.03256/) (2018)
- [Optimal load-side control for frequency regulation in smart grids](https://mlsanity.com/paper/1410.2931/) (2014)
- [An SQP Method Combined with Gradient Sampling for Small-Signal Stability Constrained OPF](https://mlsanity.com/paper/1608.03843/) (2016)
- [Real-time Flexibility Feedback for Closed-loop Aggregator and System Operator Coordination](https://mlsanity.com/paper/2006.13814/) (2020)
- [Predictability and Fairness in Social Sensing](https://mlsanity.com/paper/2007.16117/) (2020)
- [Gather-and-broadcast frequency control in power systems](https://mlsanity.com/paper/1605.09560/) (2016)
- [Unique Ergodicity in the Interconnections of Ensembles with Applications to Two-Sided Markets](https://mlsanity.com/paper/2104.14858/) (2021)

## Built on by (most cited first, 4 of 4)

- [Closed-Loop View of the Regulation of AI: Equal Impact across Repeated Interactions](https://mlsanity.com/paper/2209.01410/) (2022)
- [humancompatible.interconnect: Testing Properties of Repeated Uses of Interconnections of AI Systems](https://mlsanity.com/paper/2507.09626/) (2025)
- [Stochastic Sample Approximations of (Local) Moduli of Continuity](https://mlsanity.com/paper/2509.15368/) (2025)
- [Predictability and Fairness in Load Aggregation with Deadband](https://mlsanity.com/paper/2305.17725/) (2023)

## Abstract (arXiv)

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.