Scientific summary of the activity in 2025
The objective of this PhD thesis is to achieve a better representation of the impact that flexibilities can and will have on the needs of the future power system. Currently, long-term planning tools model these flexibilities in a highly aggregated manner, for instance by approximating a population of electric vehicles with a single “large” vehicle, or by representing all French dams with a single “Lake France.” While this approach has the advantage of greatly simplifying the solution of the associated optimization problems compared with a full system model (which would be impossible to solve), little is currently known about the error induced by such approximations and about the best way to aggregate these flexibilities. The goal of this thesis is to provide answers to these questions by combining tools from linear programming with methods from mean-field control.
The PhD is supervised on the EDF side by Olivier Beaude (R&D). On the academic side, it is supervised by Stéphane Gaubert (Tropical team, Inria Saclay), who contributes expertise in discrete optimization and tropical geometry, and by Nicolas Gast (Polaris team, Inria Grenoble), who contributes expertise in stochastic optimization and mean-field control. To carry out this project, we recruited a PhD student, Hélène Arvis, who started her thesis on November 1st, 2024.
During the year 2025, Hélène mainly studied the problem of optimizing a fleet of electric vehicles, in particular by embedding it into a \textit{Unit Commitment} problem (optimization of the electricity production–consumption balance). At the beginning of her PhD, Hélène observed that the constraints associated with a population of vehicles can be viewed as a Minkowski sum of the constraints of each individual vehicle. However, this observation alone does not make the problem tractable, since the geometry of this Minkowski sum is a priori very complex.
One of Hélène’s main contributions this year was to show that this problem can be simplified using the theory of $G$-polymatroids. This theory makes it possible to show that the geometry of the constraints is not arbitrary and to bound the number of its faces. Moreover, this characterization provides the general form of the “cuts” that must be generated by a solution algorithm in order to solve the original problem (typically a Unit Commitment) problem). This approach is promising from both a theoretical and an applied perspective. See this article for details.