Optimal pricing and charging design of the EVCS-EVs network based on a Stackelberg mean field game approach

With the rapid growth of electric vehicles (EVs) and charging networks, the design of dynamic pricing (DP) and dynamic charging (DC) strategies has become critical for maintaining grid stability and improving economic efficiency. However, traditional DP methods often fail to capture strategic interactions between electric vehicle charging stations (EVCSs) and large-scale EVs. This paper proposes a Stackelberg mean field game (SMFG) framework for the joint optimization of EVCS’s DP and EVs’ DC. The framework models the EVCS as the leader, optimizing DP via Pontryagin’s maximum principle (PMP), while EVs act as followers whose DC is described by an N -player differential game (DG) and approximated by a MFG. The mean field equilibrium is obtained by solving the coupled Hamilton–Jacobi–Bellman and Fokker–Planck–Kolmogorov equations. A hierarchical DP–DC algorithm is developed and proven to converge to a SMF ε N -Nash equilibrium (NE). Numerical results demonstrate that the proposed framework achieves efficient and scalable coordination between DP and DC decisions, while improving computational efficiency and maintaining stable system performance.