Prestigious journal Automatica has recently published two papers by researchers from the Czech Technical University in Prague and the Imperial College London, pioneering the study of predictability and fairness in load aggregation and operations of virtual power plants. These underlie the transformation of the electric power systems as we know them.

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. The papers propose 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. The papers show that this notion cannot be guaranteed with many traditional controllers used by the load aggregator, including the usual proportional–integral (PI) controller. However, 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.

In summary, the papers provide insights into how not to perform load aggregation in power systems and on the flip side, how to formulate conditions for desirable (ergodic) behavior in terms of concepts from non-linear control.

See the publications:

Jakub Mareček, Michal Roubalik, Ramen Ghosh, Robert N. Shorten, Fabian R. Wirth, Predictability and fairness in load aggregation and operations of virtual power plants, Automatica, Volume 147, 2023, 110743, ISSN 0005-1098, https://doi.org/10.1016/j.automatica.2022.110743.

Vyacheslav Kungurtsev, Jakub Marecek, Ramen Ghosh, Robert N. Shorten, On the Ergodic Control of Ensembles in the Presence of Non-linear Filters: https://doi.org/10.48550/arXiv.2112.06767.