Optimal Stochastic Management of Energy Storage Systems based on Non-linear Energy Reservoir Models

This paper discusses and extends energy-reservoir models (ERMs) for energy storage systems (ESSs), recently proposed in the related literature, by introducing a non-unitary efficiency for the discharging process. This enhancement allows the resulting ESS model to more accurately represent losses during both charging and discharging cycles, albeit at the cost of introducing a non-linearity. We show that, while the lower ERM capacity bound preserves convexity, the upper bound does not. Hence, a mixed-integer reformulation is provided to tackle such a non-convexity. We focus on the perspective of a prosumer equipped with an ERM and served by an energy retailer characterized by a realistic energy pricing scheme. We also account for the inherent uncertainty in ESS management related to the prosumer's energy demand and generation curves: to accommodate this uncertainty, our approach accepts probabilistic forecasts as inputs, enabling objective function approximation through techniques such as sample average approximation. The proposed approach is numerically validated using real data, implementing the formulation within a model-predictive-control framework.