Multi-fidelity optimization for the day-ahead scheduling of Pumped Hydro Energy Storage

Optimizing the operation of Pumped-Hydro Energy Storage (PHES) requires accurately representing nonlinearities, such as reservoir geometry and water-power conversion efficiency. While traditional methods like Mixed-Integer Linear Programming (MILP) offer theoretical guarantees, they rely on approximations that can lead to suboptimal decisions and costly redispatch or penalties. Because of its inherent approximations, MILP is a low-fidelity optimization model. In this paper, we propose a multi-fidelity approach that combines MILP with a Surrogate-Based Optimization Algorithm (SBOA). MILP solutions are used as warm-starts for the SBOA, which refines the solutions using a high-fidelity simulator of PHES dynamics and redispatch costs. This allows the SBOA to handle nonlinearities and improve the initial MILP solution by exploring areas with higher expected value. Our approach is tested on a PHES unit that participates in the energy and reserve markets in Belgium. The results show that, despite the extensive efforts made in MILP modeling, decisions can still be improved through smart integration with SBOAs.