Two recent research articles published in the prestigious journal Automatica (January 2023) provide insights into how not to perform load aggregation in power systems and on the flip side, how to formulate the conditions for ergodic behavior in terms of incremental input-to-state stability and related concepts from non-linear control.

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 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. We 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.

Results of simulations on the IEEE 118-bus test system: Powers at buses 1 and 5.

Jakub Mareček acknowledges support of the OP RDE funded project CZ.02.1.01/0.0/0.0/16_019/0000765 “Research Center for Informatics” and from the European Union’s Horizon Europe research and innovation programme under grant agreement No. GA 101070568.

Cite as

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,

Vyacheslav Kungurtsev, Jakub Marecek, Ramen Ghosh, Robert N. Shorten, On the Ergodic Control of Ensembles in the Presence of Non-linear Filters: