Along with the rapid development of electric vehicle (EV) charging technologies, many new types of charging facilities have been utilized in electric vehicle charging stations (EVCSs). Charging facilities with different rated charging power can satisfy the charging demands from diverse EV owners, and simultaneously impact the spatial and temporal distribution of EV charging demands, which in consequence challenges the rationality and economy of EVCS allocation schemes. Based on this background, this paper indicates that EVCSs should be regarded to comprise multi-types of charging facilities during the planning stage, and a new optimization model is proposed for the target of minimizing the annualized social cost of whole EV charging system. To process the complexity of the optimization model, a two-step equivalence is proposed and applied. After the equivalence and some exact relaxation, the proposed optimization model has been transformed into the type of mixed integer second-order cone programming (MISOCP), which can be efficiently solved by appropriate mathematical methods. To demonstrate the feasibility and effectiveness of the proposed approach, a practical urban area fed by a 31-bus distribution system in China has been used as the test system and the numerical results are presented and analyzed.