Decentralized Equilibrium Seeking of Joint Routing and Destination Planning of Electric Vehicles: A Constrained Aggregative Game Approach

Increasing the penetration of electric vehicles (EVs) in public transportation, which is also sped up by governments' carbon net-zero policies, will significantly increase the demand for electricity. Therefore, when we face with a large population of selfish EV users, we need a coordination mechanism to manage both the traffic congestion and electricity resource limitations. This paper introduces a novel aggregative game model where heterogeneous EVs simultaneously plan their parking lot as their destination (usually accompanied by battery charging) and the route to the destination. The cost function of users consists of factors such as traveling time, variable costs of congestion and electricity demand, and tolling which is imposed to satisfy coupling constraints such as roads' capacity and stations' power capacity. Since the users are selfish and do not reveal their objectives and personal constraints, we propose a privacy preserving decentralized algorithm with a traffic coordinator and multiple stations' coordinators for generalized Nash equilibrium (GNE) seeking of the game model. Only aggregate information such as traffic on the road and stations' energy demand are available to the traffic coordinator and charging stations' coordinators, respectively. We show that the proposed aggregative game admits a unique variational generalized Nash equilibrium (v-GNE). Then, using the theory of variational inequality (VI), we show that the proposed decentralized algorithm converges to the unique v-GNE of the game. Finally, we carry out comprehensive simulation studies on a simulated Savannah city model to compare and evaluate the proposed method.