The modern quest for sustainable cities increasingly relies on using distributed energy resources (DERs), which requires new planning practices. This paper proposes an optimisation strategy to solve the fast charging station (FCS) allocation of electric vehicles (EVs). A mixed-integer programming (MIP) model minimises investment and operation costs, considering the building of FCSs with photovoltaic (PV) systems over carports and battery energy storage systems (BESSs) as planning alternatives. The embedded set covering problem has special aspects that allow the development of a novel approach to evaluate candidate sites to accommodate FCSs. A preprocessing strategy is developed to fine-tune the entire solution space. A multiobjective approach is used to obtain an optimal compromise solution for the MIP model when it is required to serve the maximum number of EV owners at the lowest possible cost. The combined strategies reduce the computational burden, allowing full-scale studies of EV charging system planning. The results of studies using a real-world Brazilian case certify the benefits of the proposed strategy in the FCS allocation problem and in optimising the operation when considering renewable alternatives.