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

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, controllab...

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Bibliographic Details
Published inarXiv.org
Main Authors Nazir, Md Salman, Hiskens, Ian A, Bernstein, Andrey, Dall'Anese, Emiliano
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.10.2018
Subjects
Algorithms
Approximation
Computation
Computer simulation
Economic models
Energy resources
Energy sources
Energy storage
Mathematical analysis
Polytopes
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Summary: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.
ISSN:2331-8422