Optimal Location and Size of Renewable Energy Resources and Fast-Charging Stations in The Presence of Uncertainties

Due to the increasing use of electric vehicles (EVs) in transportation systems, sufficient infrastructures have to be provided to comfort the charging of the battery of EVs. The fast-charging stations (FCSs) are One of the most critical infrastructures for PEV charging that can impose a large load demand on the distribution network. Therefore, one of the original challenges in the development of EVs is the optimal allocation of FCSs. This paper presents a model for FCSs location and renewable energy resources (RESs), while the difference in the driving range, the arrival time of EVs and uncertainty of the arrival state of charge (SoC), and power generation RESs are taken into account. The proposed model minimizes the cost of installing FCSs and the development of the distribution network and maximizes the capturing of the traffic flow by the FCSs. For this purpose, first, the modeling of the uncertainties of RESs and the capacitated-flow refueling location model (CFRLM) is introduced to cover EVs. Then mixed-integer linear programming (MILP) is used for modeling the problem of locating FCSs and RESs. The proposed model is implemented on the 25-node traffic network coupled with a 14-bus distribution network. The results show that the presence of RESs and the differences and uncertainties will influence the FCSs location and size, the investment cost, and EVs coverage.