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

TL;DR

This paper introduces a union-based method for inner approximation of Minkowski sums of convex polytopes, with applications to aggregating distributed energy resources, balancing accuracy and computational complexity.

Contribution

It proposes a novel union-based approach with homothet decompositions for Minkowski sum approximation, addressing heterogeneity and complexity in energy resource aggregation.

Findings

Effective approximation of energy resource feasibility sets

Reduced computational complexity through candidate set definitions

Trade-off analysis between accuracy and efficiency

Abstract

This paper develops and compares algorithms to compute inner approximations of the Minkowski sum of convex polytopes. As an application, the paper considers the computation of the feasibility set of aggregations of distributed energy resources (DERs), such as solar photovoltaic inverters, controllable loads, and storage devices. To fully account for the heterogeneity in the DERs while ensuring an acceptable approximation accuracy, the paper leverages a union-based computation and advocates homothet-based polytope decompositions. However, union-based approaches can in general lead to high-dimensionality concerns; to alleviate this issue, this paper shows how to define candidate sets to reduce the computational complexity. Accuracy and trade-offs are analyzed through numerical simulations for illustrative examples.