While the number of internal combustion vehicles is stagnating, and is even expected to decrease in a few decades, the amount of electric vehicles is predicted to increase. Most of the electric cars are designed for daily urban use, thus in the near future, bigger cities might have some ten percentage of electric cars running on their streets during the day. And these vehicles need to be recharged in the evening or during night, so the electric vehicles, including the high performance electric cars, will interact with the power grid in this period. The impact of the charging process is predicted to be apparent on the distribution system, mostly on the low voltage grid, by influencing the network voltage profiles and the loading of the grid elements. As a practical issue we have chosen parts of the LV grid of Budapest, a city with almost two million inhabitants. If 20% of the cars is electric powered, then every fifth household has a car that has to be charged. In this paper we present the results of simulations conducted on the aforementioned grids with chargers placed at different places, using the DIgSILENT Power Factory software package. To get a better view of how electric cars' charging would affect the LV grid, we have run several load flow simulations on a large number of power grids. By statistically analyzing the obtained results, an overall picture can be acquired about the possible issues that electric car charging might have on the electric network of a large city.