Optimal charging profiles and pricing strategies for electric vehicle charging stations

In this paper, we analyze the electric vehicle charging business by modeling the charging station and the electric vehicle customer as market players. Each player maximizes his own utility by choosing the charging profile. This problem is first considered under the condition that the charging price is exogenous, where competitive equilibrium is studied. The charging profile at the competitive equilibrium maximizes the utilities of both market players simultaneously. Furthermore, a Stackelberg scenario is considered, where the charging station as a leader is able to alter the price based on the knowledge of the customer's preference. Both equilibria are characterized in the dynamic scope over a given time horizon using Pontryagin minimum principle. Moreover, the competitive equilibrium is shown to be socially optimal. The upper bound of social optimality gap of the Stackelberg equilibrium is also provided. Numerical examples are given to illustrate the results.