Robust Aggregation of Electric Vehicle Flexiblity

TL;DR

This paper develops a robust framework for characterizing and aggregating the flexibility of electric vehicle charging, accounting for uncertain requirements and providing probabilistic guarantees using measure concentration.

Contribution

It extends existing models to include uncertain charging requirements and introduces robust aggregate flexibility sets with finite sample guarantees.

Findings

Robust flexibility sets can be tightly bounded with limited samples.

The framework provides probabilistic guarantees for aggregate EV flexibility.

Numerical results validate the theoretical bounds and applicability.

Abstract

We address the problem of characterizing the aggregate flexibility in populations of electric vehicles (EVs) with uncertain charging requirements. Extending upon prior results that provide exact characterizations of aggregate flexibility in populations of electric vehicle (EVs), we adapt the framework to encompass more general charging requirements. In doing so we give a characterization of the exact aggregate flexibility as a generalized polymatroid. Furthermore, this paper advances these aggregation methodologies to address the case in which charging requirements are uncertain. In this extended framework, requirements are instead sampled from a specified distribution. In particular, we construct robust aggregate flexibility sets, sets of aggregate charging profiles over which we can provide probabilistic guarantees that actual realized populations will be able to track. By leveraging measure concentration results that establish powerful finite sample guarantees, we are able to give tight bounds on these robust flexibility sets, even in low sample regimes that are well suited for aggregating small populations of EVs. We detail explicit methods of calculating these sets. Finally, we provide numerical results that validate our results and case studies that demonstrate the applicability of the theory developed herein.