Multi-stall fast charging stations are often thought to require megawatt-range grid connections. The power consumption profile of such stations results in high cost penalties due to monthly power peaks and expensive linkage fees. A local energy storage system (ESS) can be used to address peak power demands. However, no appropriate sizing method is available to match specific constraints, such as the contracted power available from the grid and the projected recharging demand. A stochastic distribution of charging events was used in this paper to model power demand profiles at the station, with a one minute resolution. Based on 100 simulated months, we propose an optimum number of charging points, and we developed an algorithm to return the required local ESS capacity as a function of the available grid connection. The role of ESSs in the range of 100 kWh to 1 MWh was studied for all stations with up to 2000 charging events per week. The relevance of ESS implementation was assessed along three parameters: the number of charging points, the available grid connection, and the ESS capacity. This work opens new possibilities for multi-stall charging station deployment in locations with limited access to the medium voltage grid, and provides sizing guidelines for effective ESSs implementation. In addition, it helps build business cases for charging station operators in regions with high demand charges.