The increasing number of electric vehicles poses new challenges to the power grid. Their charging process stresses the power system, as additional energy has to be supplied, especially during peak load periods. This additional load can result in critical network situations depending on various parameters. These impacts may vary based on market penetration, the energy demand, the plug-in time, the charging rate, and the grid topology and the associated operational equipment. Hence, the impact of electric vehicles (EVs) on the power grid was analysed for twelve typical German low voltage grids by applying power flow calculations. One main result was that thermal and voltage-related network overloads were highly dependent on market penetration and grid topology.