© 2022 IEEE.Conventional internal combustion engine vehicles are one of the main reasons for the increase in carbon emissions. The Electric Vehicles (EVs) in the transportation sector to significantly reduce these emissions, can be expanded collectively instead of these vehicles. While EVs are still hindered from adoption due to their battery life, cost and few other challenges, the global fuel crisis around the world, sanctions and incentives in government policies are helping large-scale EVs adoption. The increase in EVs penetration adds an indefinite amount of electricity to the grid and is likely to pose a very complex operating problem for distribution grid operators. Since EV users want to leave with maximum battery energy capacity, uncoordinated charging can damage grid equipment in the distribution system. Accurate charge scheduling of EVs is essential for seamless integration of EVs into the grid. However, in this charging scheduling, it is necessary to consider the battery energy capacities of the EVs as well as the charging costs. In this paper, the optimal charging scheduling of EVs under the proposed smart coordination was performed according to the battery capacity. In this way, uncoordinated charging was prevented, which led to an increase in the peak power of the distribution system. Data for EV charging time, waiting time and battery energy-capacity were obtained by Monte Carlo Simulations (MCSs) based on statistical data. The Mixed Integer Linear programming (MILP) technique was used for charging scheduling of EVs. The results show that the proposed approach is a systematic reference, as it both reduces the charging cost of the users when charging the EVssand efficiently uses the load smoothing and load-shifting strategies in the distribution network.