As China proposes to achieve carbon peak by 2030 and carbon neutrality by 2060, as well as the huge pressure on the power grid caused by the load demand of the energy supply stations of electric vehicles (EVs), there is an urgent need to carry out comprehensive energy management and coordinated control for EVs’ energy supply stations. Therefore, this paper proposed a two-step intelligent control method known as ISOM-SAIA to solve the problem of the 24 h control and regulation of green/flexible EV energy supply stations, including four subsystems such as a photovoltaic subsystem, an energy storage subsystem, an EV charging subsystem and an EV battery changing subsystem. The proposed control method has two main innovations and contributions. One is that it reduces the computational burden by dividing the multi-dimensional mixed-integer programming problem of simultaneously optimizing the 24 h operation modes and outputs of four subsystems into two sequential tasks: the classification of data-driven operation modes and the rolling optimization of operational outputs. The other is that proper carbon transaction costs and carbon emission constraints are considered to help save costs and reduce carbon emissions. The simulation analysis conducted in this paper indicates that the proposed two-step intelligent control method can help green/flexible EV energy supply stations to optimally allocate energy flows between four subsystems, effectively respond to peak shaving and valley filling of power grid, save energy costs and reduce carbon emissions.