Exact Recourse Functions for Aggregations of EVs Operating in Imbalance Markets

TL;DR

This paper introduces a novel, dimension-reducing approach to optimize the charging of large EV fleets in imbalance markets by deriving exact recourse functions and policies through geometric and stochastic analysis.

Contribution

It presents a new method that leverages permutahedron geometry to efficiently solve multistage stochastic programs for EV aggregation, overcoming scalability issues.

Findings

Exact recourse functions characterized as piecewise affine.

Closed-form expressions for affine region parameters.

Numerical validation confirms practical effectiveness.

Abstract

We study optimal charging of large electric vehicle populations that are exposed to a single real-time imbalance price. The problem is naturally cast as a multistage stochastic linear programme (MSLP), which can be solved by algorithms such as Stochastic Dual Dynamic Programming. However, these methods scale poorly with the number of devices and stages. This paper presents a novel approach to overcome this curse of dimensionality. Building prior work that characterises the aggregate flexibility sets of populations of EVs as a permutahdron, we reformulate the original problem in terms of aggregated quantities. The geometric structure of permutahedra lets us (i) construct an optimal disaggregation policy, (ii) derive an exact, lower-dimensional MSLP, and (iii) characterise the expected recourse function as piecewise affine with a finite, explicit partition. In particular, we provide closed-form expressions for the slopes and intercepts of each affine region via truncated expectations of future prices, yielding an exact form for the recourse function and first-stage policy. Comprehensive numerical studies validate our claims and demonstrate the practical utility of this work.