Fast and random charging of electric vehicles (EVs) in the charging station can easily cause the overload and uncertain peak load of the grid. In order to improve the stability of the grid and reduce the power fluctuation caused by random charging, a charging load discrete model for energy storage configuration is proposed. The time-continuous charging load curve is discretized into charging sequences at equal intervals, the power supply cap of the grid and energy storage capacity are quantified to the number of available charging piles, and the load status is described by applying queuing theory within the set time. Then the system load state transition relation is established by applying two-dimensional discrete time Markov chain, thus a random charging model of a single energy storage fast charging station is established. According to the state space and probability distribution of the discretized load, the economics under different load statuses are analyzed. Finally, through the case study, the impact of the EV arrival rate on the service quality and economy is analyzed under different ratios of grid power and energy storage power, so that the feasibility of the model is verified.