Exact Aggregate Models for Optimal Management of Heterogeneous Fleets of Storage Devices

Future power grids will entail large fleets of storage devices capable of scheduling their charging/discharging profiles so as to achieve lower peak demand and reduce energy bills, by shifting absorption times in synchronous with the availability of renewable energy sources. Optimal management of such fleets entails large-scale optimization problems which can be dealt with in a hierarchical manner by clustering together individual devices into fleets. Based on recent results characterizing the set of aggregate demand profiles of a heterogeneous fleet of charging devices, an exact aggregate model is proposed to achieve optimality, in a unit commitment problem, by adopting a simplified formulation with a number of constraints for the fleet that scales linearly in the number of time-slots and is independent of the size of the fleet. This is remarkable, as it shows that under suitable conditions, a heterogeneous fleet of any size can effectively be treated as a single storage unit.