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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Published in | arXiv.org |
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Main Authors | , , , |
Format | Paper |
Language | English |
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Cornell University Library, arXiv.org
03.10.2018
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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. |
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AbstractList | 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. |
Author | Dall'Anese, Emiliano Bernstein, Andrey Hiskens, Ian A Nazir, Md Salman |
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SubjectTerms | Algorithms Approximation Computation Computer simulation Economic models Energy resources Energy sources Energy storage Mathematical analysis Polytopes |
Title | Inner Approximation of Minkowski Sums: A Union-Based Approach and Applications to Aggregated Energy Resources |
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