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 system operator to balance the additional load. Fast and high-power density of batteries makes them a conceivable option for this task, if properly sized. Charging profile of EVs is constructed by considering travel pattern, charging need and driver's behaviour of EVs. Moreover, a sizing algorithm is proposed to compute the battery capacity for parking lots equipped with EV chargers in a constrained grid. The proposed sizing algorithm ensures 1) balance the EV load, 2) avoid over/under-sizing of the system. The accuracy of the proposed battery sizing algorithm is shown by simulation results, characterised by using real data of household travel survey and parking occupancy data.