Interpretable Distributionally Robust Optimization for Battery Energy Storage System Planning

A mathematical programming approach rooted in distributionally robust optimization (DRO) provides an effective data-driven strategy for battery energy storage system (BESS) planning. Nevertheless, the DRO paradigm often lacks interpretability in its results, obscuring the causal relationships between data distribution characteristics and the outcomes. Furthermore, the current approach to battery type selection is not included in traditional BESS planning, hindering comprehensive optimization. To tackle these BESS planning problems, this paper presents a universal method for BESS planning, which is designed to enhance the interpretability of DRO. First, mathematical definitions of interpretable DRO (IDRO) are introduced. Next, the uncertainties in wind power, photovoltaic power, and loads are modeled by using second-order cone ambiguity sets (SOCASs). In addition, the proposed method integrates selection, sizing, and siting. Moreover, a second-order cone bidirectional-orthogonal strategy is proposed to solve the BESS planning problems. Finally, the effectiveness of the proposed method is demonstrated through case studies, offering planners richer decision-making insights.