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

2018/10/03 by Md Salman Nazir, Nazir, Md Salman, Ian A. Hiskens +5 · 3 citations
Mathematics · Computer Science · #Advanced Optimization Algorithms Research #Graph theory and applications #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.1810.01587

Abstract

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

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