A Coupled Game Theory and Lyapunov Optimization Approach to Electric Vehicle Charging at Fast Charging Stations

The development of electric vehicle (EV) charging stations has been a key consideration for enabling the evolution of EV technology and continues to support the fosterage of this technology. Notably, fast charging enhances the EV user's adaptability by reducing the charging time and supporting long-mile travel. The optimal operation and erratic power demand of a fast charging station (FCS) are still challenging. It is necessary to understand EV charging scheduling and FCS management, which can jointly overcome the problem of EV users on account of optimal operation. However, joint optimization needs detailed future information, which is a formidable task for prediction. This paper aims to address the joint optimization issue using combined game theory and the Lyapunov optimization approach. This hybrid approach could ease the data forecast requirement and minimize the operating costs of FCSs while optimally dispatching EVs to FCSs and satisfying their energy demand. Further, the problem is decomposed into three subproblems. The first subproblem addresses a network of FCSs that try to maximize their revenue through a dynamic pricing game with EV customers who have different behavioral responses to the prices. The pricing game determines the electricity selling prices in a distributed manner as well as the energy demand of users. Subsequently, EVs are assigned to local FCSs, taking into account the distance from and the queue at the stations. Finally, the third subproblem exploits Lyapunov optimization to control the operation cost of each FCS, considering the impact of demand charges. In this paper, the proposed method is validated through a numerical analysis using the real data of FCSs in Boulder, Colorado. Moreover, the presented results revealed that the proposed method is efficient regarding dynamic pricing and optimal allocation of EVs to stations.