Energy Storage Sizing in Presence of Uncertainty

Uncertainty is an inevitable side-effect of the increasing penetration of intermittent energy sources like solar and wind into the power grid. Since energy storage systems (ESS) can be employed to mitigate the effect of uncertainties, their energy and power ratings along with their charging control strategies become of vital importance for renewable energy producers. This work deals with the task of sizing under a model predictive control (MPC) operation for a single ESS used to smoothen out a random energy signal. To account for correlations in the energy signal and enable charging adjustments in response to real-time fluctuations, we adopt a linear charging policy. The policy is designed by minimizing the initial ESS investment plus the average operational cost. Since charging decisions become random, the energy and power limits are posed as chance constraints. Relying on first- and second-order moments for the energy signal, the chance constraints are enforced in a distributionally robust fashion. To better approximate the joint probability of acquiring feasible charging schedules, the double-sided ESS limits are handled jointly as second-order cone constraints. The proposed scheme is contrasted to a charging policy under Gaussian uncertainties and a deterministic formulation.