A Conic Relaxation Approach for Solving Stackelberg Pricing Game of Electric Vehicle Charging Station Considering Traffic Equilibrium

In recent years, the number of electric vehicles (EVs) and fast charging stations has increased rapidly. Generally, self-interested charging station operators in urban transportation networks aim to maximize their profits by optimizing charging price strategies, while EV users aim to minimize their travel costs via routing and charging station choices. The non-cooperative interaction between charging station operators and EV users forms a Stackelberg game. To obtain the optimal pricing of fast charging stations, it is necessary to solve a mathematical program with complementarity constraints, which is non-convex and difficult to solve. In this study, a conic relaxation method is proposed to relax the original problem. If certain dual variables are non-negative, the proposed conic relaxation is exact. Furthermore, if users’ routing choices are more likely to be irrational, or perfectly rational and meanwhile almost all the EV users with the same origin-destination pair choose one same path, then the conic relaxation is more likely to be exact. Under other conditions, a penalty convex concave procedure is employed to obtain an optimal or near-optimal solution to the original problem based on the solution of the relaxed problem. A mathematical proof is provided, and numerical tests verify the efficacy of the method.