Integrating Aggregated Electric Vehicle Flexibilities in Unit Commitment Models using Submodular Optimization

TL;DR

This work addresses integrating aggregated EV flexibilities into deterministic unit-commitment problems by exploiting the generalized polymatroid structure of EV constraint sets. It proves that the convex UC with EV can be solved via a polyhedral-separation oracle in time that scales with $O(d^3 \log(dBN))$ calls, yielding an overall $O(N \log N)$ dependence on the number of EV profiles, and introduces a practical cutting-plane algorithm based on submodular optimization. Numerical tests on a European ERAA dataset and a French EV fleet data demonstrate rapid convergence (often under 8 iterations) and show that the separation oracle dominates runtime, while the approach remains far below the theoretical facet bound of $2^{\mathcal{T}+1}$. The results establish a scalable, exact method to incorporate EV flexibility into long-horizon UC with realistic data, enabling more accurate planning for grids with high renewable penetration.

Abstract

The Unit Commitment (UC) problem consists in controlling a large fleet of heterogeneous electricity production units in order to minimize the total production cost while satisfying consumer demand. Electric Vehicles (EVs) are used as a source of flexibility and are often aggregated for problem tractability. We develop a new approach to integrate EV flexibilities in the UC problem and exploit the generalized polymatroid structure of aggregated flexibilities of a large population of users to develop an exact optimization algorithm, combining a cutting-plane approach and submodular optimization. We show in particular that the UC can be solved exactly in a time which scales linearly, up to a logarithmic factor, in the number of EV users when each production unit is subject to convex constraints. We illustrate our approach by solving a real instance of a long-term UC problem, combining open-source data of the European grid (European Resource Adequacy Assessment project) and data originating from a survey of user behavior of the French EV fleet.

Figures (3)

• Figure 1: Number of iterations performed by \ref{['cutting_planes']}. The error bar represents extreme values obtained, as well as the average value. Despite an increase with problem size, the iteration number remains low.
• Figure 2: Number of cuts added to UC. There is no point for $N=2$ at $T=24$ as every simulation converged in 1 iteration. All values are much smaller than the theoretical $2^{T+1}$ bound.
• Figure 3: Resolution time as a function of $T$ and $N$. As expected, it increases with $T$ and $N$.

Theorems & Definitions (17)

• Definition 1
• Definition 2
• Definition 3
• Theorem 1
• Theorem 2: koshevoy_personnal_2025mukhi_exact_2025
• Remark
• Definition 4
• Theorem 3
• Theorem 4
• Remark