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Electric vehicles (EVs) will be dominating the modes of transport in the future. Current limitations discouraging the use of EVs are mainly due to the characteristics of the EV battery and lack of easy access to charging stations. Charging schedules of EVs are usually uncoordinated, whereas coordinated charging offers several advantages, including grid stability. For a solar photovoltaic (PV)-based charging station (CS), optimal utilization of solar power results in an increased revenue and efficient utilization of related equipment. The solar PV and the arrival of EVs for charging are both highly stochastic. This work considers the solar PV forecast and the probability of EV arrival to optimize the operation of an off-grid, solar PV-based commercial CS with a battery energy storage system (BESS) to realize maximum profit. BESS supports the sale of power when the solar PV generation is low and subsequently captures energy from the solar PV when the generation is high. Due to contrasting characteristics of the solar PV and EV charging pattern, strategies to maximize the profit are proposed. One such strategy is to optimally size the BESS to gain maximum profit. A mixed integer linear programming (MILP) method is used to determine the optimal solution.