Generalized Wardrop Equilibrium for Charging Station Selection and Route Choice of Electric Vehicles in Joint Power Distribution and Transportation Networks

This article presents the equilibrium analysis of a game composed of heterogeneous electric vehicles (EVs) and a power distribution system operator (DSO) as the players, and charging station operators (CSOs) and a transportation network operator (TNO) as coordinators. Each EV tries to pick a charging station as its destination and a route to get there at the same time. However, the traffic and electrical load congestion on the roads and charging stations lead to the interdependencies between the optimal decisions of EVs. CSOs and the TNO need to apply some tolling to control such congestion. On the other hand, the pricing at charging stations depends on real-time distributional locational marginal pricing, which is determined by the DSO after solving the optimal power flow over the power distribution network. This article also takes into account the local and the coupling/infrastructure constraints of EVs, along with transportation and distribution networks. This problem is modeled as a generalized aggregative game, and then a decentralized learning method is proposed to obtain an equilibrium point of the game, which is known as variational generalized Wardrop equilibrium. The existence of such an equilibrium point and the convergence of the proposed algorithm to it are proven. We undertake numerical studies on the Savannah city model and the IEEE 33-bus distribution network and investigate the impact of various characteristics on demand and prices.