Charging of electric vehicles (EVs) significantly impact the reliability of the power system. A constrained power grid is a feasible solution to maintain the reliability of the power system. However, in a constrained power grid, it is challenging for the parking lot operator to balance the additional load. The fast and high-power density of batteries makes them a conceivable option for this task if adequately sized. A sizing algorithm is proposed to compute the battery capacity for parking lots while considering the intermittent usage of EVs in a constrained grid. Charging profile of EVs is constructed by considering travel pattern, charging need and driver's behaviour of EVs. The proposed sizing algorithm avoided over/under-sizing of the battery energy storage system and fulfilled the EV charging demand in the parking lot. The accuracy of the proposed battery sizing algorithm is shown by simulation results, characterized by real data of household travel survey and parking occupancy data.