Coupling a Power Dispatch Model with a Wardrop or Mean-Field-Game Equilibrium Model

In this paper, we propose an approach for coupling a power network dispatch model, which is part of a long-term multi-energy model, with Wardrop or Mean-Field-Game (MFG) equilibrium models that represent the demand response of a large population of small "prosumers" connected at the various nodes of the electricity network. In a deterministic setting, the problem is akin to an optimization problem with equilibrium constraints taking the form of variational inequalities or nonlinear complementarity conditions. In a stochastic setting, the problem is formulated as a robust optimization with uncertainty sets informed by the probability distributions resulting from an MFG equilibrium solution. Preliminary numerical experimentations, using heuristics mimicking standard price adjustment techniques, are presented for both the deterministic and stochastic cases.