In distribution networks, failure to smooth the load curve leads to voltage drop and power quality loss. In this regard, electric vehicle batteries can be used to smooth the load curve. However, to persuade vehicle owners to share their vehicle batteries, we must also consider the owners' profits. A challenging problem is that existing methods do not take into account the vehicle owner demands including initial and final states of charge and arrival and departure times of vehicles. Another problem is that battery capacity of each vehicle varies depending on the type of vehicle; which leads to uncertainties in the charging and discharging dynamics of batteries. In this paper, we propose a modified mean-field method so that the load curve is smoothed, vehicle owner demands are met, and different capacities of electric vehicle batteries are considered. The simulation results show the effectiveness of the proposed method.