Optimal Sizing and Operation of Shared Energy Storage in Microgrids: A Distributionally Robust Stackelberg Game

To address the operational risks caused by the high penetration of distributed renewable energy and the underutilization of demand-side flexibility in microgrids, this paper proposes an optimal sizing and operation framework for Shared Energy Storage Systems (SESS) based on a distributionally robust Stackelberg game. Specifically, a high-order Resistance-Capacitance (RC) network model is introduced to quantify building thermal inertia, enabling Integrated Buildings (IBs) to function as flexible thermal loads. A bilevel optimization model is formulated wherein the SESS acts as the leader maximizing profit, while IBs act as followers optimizing power dispatch and thermal comfort. Furthermore, a data-driven distributionally robust optimization (DRO) approach constructing an ambiguity set via historical moment information is employed to handle renewable uncertainty, and the bilevel problem is reformulated into a tractable Mixed-Integer Linear Programming (MILP) model via Karush-Kuhn-Tucker (KKT) conditions. Case studies demonstrate that the proposed method effectively coordinates source-load-storage resources, significantly reducing total costs and load shedding risks compared to deterministic and stochastic approaches.