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This paper develops and compares algorithms to compute inner approximationsof the Minkowski sum of convex polytopes. As an application, the paperconsiders the computation of the feasibility set of aggregations of distributedenergy resources (DERs), such as solar photovoltaic inverters, controllableloads, and storage devices. To fully account for the heterogeneity in the DERswhile ensuring an acceptable approximation accuracy, the paper leverages aunion-based computation and advocates homothet-based polytope decompositions.However, union-based approaches can in general lead to high-dimensionalityconcerns; to alleviate this issue, this paper shows how to define candidatesets to reduce the computational complexity. Accuracy and trade-offs areanalyzed through numerical simulations for illustrative examples.

Inner Approximation of Minkowski Sums: A Union-Based Approach and Applications to Aggregated Energy Resources