A Discounted Stochastic Multiplayer Game Approach for Vehicle-to-Grid Voltage Regulation

Along with the diversification of electricity market, the voltage regulation (VR) service is opened up to various qualified providers to meet the enormous demand, among which, the electric vehicle (EV) aggregators (AGGs) can integrate the scattered EVs and play the role of VR sources with a high response speed and low cost. In order to coordinate the VR service providers to satisfy the total VR requirement, auction mechanisms are widely used to select VR sources to achieve better performance. Yet, it is challenging to optimize the strategy of each EV AGG in the auction process due to the stochastic EV mobility, various distribution network topology, and the competition mechanism. To address these challenges, we proposed a discounted stochastic multiplayer game (DSMG) approach to analyze the competition among EV AGGs. Due to the constraint of distribution network topology, the efficiency of the VR sources at different locations can be different. Thus, the impact of distribution network topology on the VR efficiency is investigated by DSO when evaluating the capacity of AGGs. The randomness of EV numbers is considered when predicting the AGGs' available VR capacity so that the tendency for the AGGs to follow the optimal strategies can be modeled accurately. Accordingly, a linear power flow analysis approach and a battery pool model are developed to address the distribution network topology and EV mobility, respectively. Then, the DSMG approach is used in the VR auction process to optimize the AGGs' strategies. The existence proof of the stationary Markov perfect equilibrium is presented, and the corresponding algorithms to obtain the equilibrium is proposed. The performance of the proposed DSMG approach is evaluated and compared with other approaches based on the IEEE 33-bus test feeder, IEEE 123-bus test feeder, and the real-world generation and load data from PVWatts Calculator and Market Analysis and Information System, respectively.