A hierarchical distributed energy management for multiple photovoltaic (PV) based electric vehicle (EV) charging stations (PV-CSs) is proposed and analyzed in this paper. In the station level, PV-CSs are modelled as independent players with objectives to stabilize their average available capacity (AAC) of the storage battery tank. Meanwhile, in EV level, EV owners are modeled as players with objectives to maximize their charging power. Then a two level power distribution game is utilized to model the power distribution problem in both station and EV level. Through utilizing a consensus network based learning algorithm, a cooperative and a generalized Stackelberg equilibrium are achieved in station and EV level through a distributed fashion. One case studies, i.e., two station case, is implemented in simulation to verify the performance and effectiveness of the proposed strategy. The simulation results show that the proposed energy management has an excellent performance in both cases and comparing against stations without management.