The availability of publicly accessible charging sta- tions in urban areas can foster the widespread adoption of Electric Vehicles (EVs). However, the introduction of public charging infrastructures will put an additional strain on the power grid due to the possible occurrence of peak demands. This study is a first attempt to quantitatively assess the potential benefits of introducing in a public charging infrastructure smart charging stations that are capable of modulating the current supplied to the EVs. Specifically, we assume that each charging station has limited power resources that must be shared among the EVs attached to its charging sockets according to a given scheduling strategy. To evaluate the performance of such system we utilise SUMO, an open-source and widely used vehicular traffic simulator, along with a highly realistic mobility trace for the metropolitan area of Luxembourg City. Simulation results indicate that the use of simple charging strategies that take advantage of the modulation capabilities of smart charging stations (e.g., fair-sharing or token-based scheduling approaches) can effectively mitigate the impact of EV charging demands on the power grid with a limited degradation of charging performance. However, our results also confirm that a significant investment on charging infrastructure might be necessary to guarantee a non-blocking charging service.