Wind and solar energy will play an important role in the decarbonization of the European electricity generation. However, high shares of these variable renewable energies (VREs) challenge the power system considerably due to their temporal fluctuations and geographical dispersion. In this paper, we systematically analyze transmission grid extensions as an integration measure for VREs in Europe. We show the effects of grid extensions for fundamental properties of the power system as a function of the penetration and mix of wind and solar energy. Backup capacity requirements and overproduction are reduced with a powerful overlay transmission grid. We determine the costs of the grid extensions in dependence of the VRE penetration and mix and find that the grid integration costs remain below 25% of the VRE investment costs for all conceivable VRE configurations. Furthermore, robust design features of future power systems in terms of grid geometry and flexibility requirements for backup technologies are identified. We apply a spatially and temporally highly resolved techno-economic model of the European power system for our analysis. (C) 2011 Elsevier Ltd. All rights reserved.