Mean-Field Learning for Storage Aggregation

Distributed energy storage devices can be aggregated to provide operational flexibility for power systems. This requires representing a massive device population as a single, tractable surrogate that is computationally efficient and accurate. However, surrogate identification is challenging due to heterogeneity, nonconvexity, and high dimensionality of storage devices. To address these challenges, this paper develops a mean-field learning framework for storage aggregation. We interpret aggregation as the average behavior of a large storage population and show that, as the population grows, aggregate performance converges to a unique, convex mean-field limit, enabling tractable population-level modeling. This convexity further yields a price-responsive characterization of aggregate storage behavior and allows us to bound the mean-field approximation error. We construct a convex surrogate model with physically interpretable parameters that approximates the aggregate behavior of large storage populations and can be embedded directly into power system operations. Surrogate parameter identification is formulated as an optimization problem using historical price-response data, and we adopt a gradient-based algorithm for efficient learning. Case studies validate the theoretical findings and demonstrate the effectiveness of the proposed framework in approximation accuracy and data efficiency.