Comparative Evaluation of MILP, MPC, and Reinforcement Learning for Commercial Battery Dispatch Under Time-of-Use Tariffs

Abstract

Battery energy storage systems (BESS) paired with rooftop photovoltaics (PVs) can deliver measurable cost savings under time-of-use (TOU) electricity tariffs; however, the relative performance of model-based and model-free dispatch strategies remains insufficiently benchmarked on full-year, real-world commercial datasets. This paper presents a full-year (2023) comparative evaluation of three BESS dispatch approaches using data from a commercial PV installation operating under a TOU tariff. The examined strategies include: (i) a mixed-integer linear programming (MILP) formulation with perfect foresight, providing an oracle performance benchmark under the assumed model; (ii) a model predictive control (MPC) scheme based on a day-ahead persistence forecast, representing a low-complexity deployable approach; and (iii) a soft actor-critic (SAC) deep reinforcement learning agent trained under causal information constraints. The MILP benchmark achieves an annual cost reduction of 24.6\% relative to a no-storage baseline. The persistence-based MPC approach recovers 99.2\% of this benchmark using only prior-day data. In contrast, the evaluated SAC agent yields an annual cost higher than the no-storage baseline. This outcome is analyzed in the context of known challenges in reinforcement learning for energy systems, including limited observability and reward design. Overall, the results indicate that, for the studied dataset and tariff structure, persistence-based MPC captures nearly all achievable economic benefits under practical deployment constraints, whereas the considered RL configuration does not yield competitive performance under the same information limitations.