A midway charging strategy for electric vehicles based on Stackelberg game considering fair charging

With the rapid development of the electric vehicle industry, there are games about charging between electric vehicles (EVs) and charging stations (CSs) that have been extensively studied. Due to the mileage problem that EVs still have, this paper addresses the charging interactions between EVs and CSs in a midway charging scenario. Firstly, in the information exchange process with the involvement of navigation system, each EV chooses under the influence of the pricing strategy of CSs to minimize the expenditure after considering factors including distance and road conditions. After getting EVs' strategy, CSs will adjust the charging strategy to maximize the revenue while obtaining the minimum load factor. Then, we use a Stackelberg game with multi-leader and multi-follower to model the interaction between CSs and EVs. Moreover, considering the particularity of midway charging, we add fair charging to limit the charging capacity of EVs. Lastly, to address the Stackelberg equilibrium problem, the backward induction method is adopted, that is, we derive the charging capacity strategies of EVs (i.e., followers) given the charging price of CSs (i.e., leaders), and then design the optimal pricing strategy of CSs based on the EVs' optimal strategy. Besides, a distributed algorithm is also proposed to obtain the game equilibrium iteratively. Furthermore, the simulation results show that the average charging cost of EVs is reduced by 25% using the proposed strategy, and the load balance of CSs is relatively high, which shows the effectiveness of this strategy in reducing costs and balancing loads.