The negative environmental impacts of using fossil fuel-powered vehicles underlined the need for inventing an alternative eco-friendly transportation fleet. Electrical vehicles (EVs) were introduced as an eligible substitute for the conventional vehicle fleet. The significant uncertainties associated with EVs usage, however, make their performance unpredictable. In this paper, we introduce a methodological framework for scheduling smart charging of EVs which considers the colligated uncertainties. Furthermore, the framework includes an ecumenical model for charging and discharging of EVs which is utilized in a 21-node sample distribution network which contains wind turbine as a Distributed Generation units. Our proposed approach extracted that the welfare of Vehicle to Grid effectuation in the network is much more beneficial than the uncoordinated mode. The simulation result indicates that smart charging effectuation is economical.