Scalable Computation of 2D-Minkowski Sum of Arbitrary Non-Convex Domains: Modeling Flexibility in Energy Resources

TL;DR

This paper introduces a scalable algorithm for computing the Minkowski sum of non-convex, heterogeneous energy resource flexibility domains, enabling efficient modeling of aggregated DER flexibility with guaranteed accuracy.

Contribution

It presents a novel scalable method for approximating the Minkowski sum of complex, non-convex flexibility sets in energy resources, with proven complexity bounds.

Findings

The algorithm guarantees a superset of the true Minkowski sum.

Under certain conditions, the complexity is linear with the number of resources.

Numerical examples demonstrate the method's effectiveness in diverse scenarios.

Abstract

The flexibility of active ($p$) and reactive power ($q$) consumption in distributed energy resources (DERs) can be represented as a (potentially non-convex) set of points in the $p$-$q$ plane. Modeling of the aggregated flexibility in a heterogeneous ensemble of DERs as a Minkowski sum (M-sum) is computationally intractable even for moderately sized populations. In this article, we propose a scalable method of computing the M-sum of the flexibility domains of a heterogeneous ensemble of DERs, which are allowed to be non-convex, non-compact. In particular, the proposed algorithm computes a guaranteed superset of the true M-sum, with desired accuracy. The worst-case complexity of the algorithm is computed. Special cases are considered, and it is shown that under certain scenarios, it is possible to achieve a complexity that is linear with the size of the ensemble. Numerical examples are provided by computing the aggregated flexibility of different mix of DERs under varying scenarios.