Inner Approximation of Minkowski Sums: A Union-Based Approach and Applications to Aggregated Energy Resources: Preprint
- University of Michigan
- National Renewable Energy Laboratory (NREL), Golden, CO (United States)
This paper develops and compares algorithms to compute the inner approximation of Minkowski sum of convex polytopes. We consider flexibility from distributed re- sources, such as solar photovoltaic (PV) inverters, demand side resources, etc. A polytopic representation of a single inverter's feasible operating region is proposed first. The aggregate flexibility can be computed using the Minkowski sum. Homothet and Zonotope-based approaches have been explored in literature. We show that as heterogeneity increases, such approaches lead to conservative estimates. Hence, we show how to exploit union-based Minkowski sum computation through successive homothetic decomposition of polytopes. While the union-based approach can lead to dimensionality issues, we show how to limit the complexity by predefining a candidate set. Efficiency, accuracy and trade-offs have been analyzed. Numerical examples have been presented to illustrate the effectiveness of the proposed algorithm.
- Research Organization:
- National Renewable Energy Lab. (NREL), Golden, CO (United States)
- Sponsoring Organization:
- U.S. Department of Energy Advanced Research Projects Agency-Energy (ARPA-E)
- DOE Contract Number:
- AC36-08GO28308
- OSTI ID:
- 1501668
- Report Number(s):
- NREL/CP-5D00-73423
- Resource Relation:
- Conference: Presented at the 2018 IEEE Conference on Decision and Control (CDC), 17-19 December 2018, Miami Beach, Florida
- Country of Publication:
- United States
- Language:
- English
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