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Driven by decreasing prices for photovoltaic (PV) systems and incentive programs of different governments, almost 100 GW of PV and over 100 GW of wind turbines (WT) have been integrated in the European power system by 2014. In some areas, the electricity generation already exceeds the demand, curtailing generation or pushing the existing power transmission infrastructure to its limits in certain hours. In order to reach the European Commission's targets for 2050, the integration of renewable energies will require flexibility sources, independent of conventional generation, in order to provide standard security of supply. Together different flexibility sources will ensure the match between demand and supply at any given time. Energy storage systems can provide this flexibility by shifting the load temporally while transmission grids provide the shift of load spatially. Up to a certain extent, transmission capacity and storage capacity can replace each other, i.e. storage can reduce the load on transmission infrastructure by mitigating local peaks in load and/or generation. For the transition to a fully renewable energy system by 2050, major changes have to be achieved in the structure of the power system. The planning tool GENESYS is a holistic approach that optimises the allocation and size of different generation technologies, storage systems and transnational transmission corridors of a European power system. The source code for the mentioned tool is available free of charge under LGPL license. It can be freely parameterized by the user which allows the study of different power systems under individual assumptions with regard to load, generation potential and cost of the different system components. This publication will give an introduction to the planning methodology, the system model and the optimisation approach. Optimisation results obtained with GENESYS for a fully renewable electricity system for Europe and a cost structure expected for 2050 will be presented together with sensitivity analyses ...