Stochastic Convex Optimization for Day-Ahead Shared Battery Storage Scheduling in Solar Energy Communities

Energy communities represent a transformative paradigm for decentralized renewable energy integration, enabling collective investment in photovoltaic (PV) systems and battery energy storage systems (BESS) to achieve economic and environmental benefits. However, the optimal operation of these communities faces significant challenges due to inherent uncertainties in solar generation, load consumption, and electricity prices. This paper presents a stochastic optimization framework for day-ahead scheduling of shared battery energy storage in solar-powered energy communities under multiple uncertainty sources. The problem is formulated as a stochastic mixed-integer nonlinear programming (MINLP) model that minimizes the expected daily operational cost, including energy procurement from the grid, PV operation and maintenance (O&M), battery operation costs, and degradation-induced expenses. A battery degradation model based on equivalent full-cycle counting captures the economic impact of cycling under uncertain conditions. The proposed approach employs a scenario-based Monte Carlo method to represent uncertainties and reformulates the MINLP as a mixed-integer linear program (MILP) through exact linearization of the absolute-value terms in the degradation cost, enabling efficient solution with commercial solvers. The framework is applied to an aggregated energy community whose installed PV capacity (6.888 MW) and shared BESS capacity (2.1667 MWh) are defined from the resource distribution of a modified IEEE 33-bus network; the aggregation focuses on the energy-time dimension of the scheduling problem, and network voltages, branch flows and locational losses are not represented. The value of the stochastic solution (VSS) is 2319.74 USD/day, showing that the stochastic schedule is substantially cheaper than the deterministic schedule when evaluated on the same uncertain scenario set. A robustness study over 30 random seeds gives an expected cost of 11,825.77 ± 295.83 USD/day. Relative to the no-storage baseline, the shared BESS reduces the expected daily cost by about 1.2%, and the terminal-SoC relaxation reduces the cost by a further 194.61 USD/day. The MILP formulation and its continuous relaxation produce the same optimum, confirming that the binary variables are not needed at the optimum.