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The future European energy supply system will have a high share of renewable energy sources (RES) to meet the greenhouse gas emission policy of the European Commission. Such a system is characterized by the need for a strongly interconnected energy transport grid as well as a high demand of energy storage capacities to compensate the time fluctuating characteristic of most RE generation technologies. With the RE generators at the location of high harvest potential, the appropriate dimension of storage and transmission system between different regions, a cost efficient system can be achieved. To find the preferred target system, the optimization tool GENESYS (Genetic Optimization of a European Energy System) was developed. The example calculations under the assumption of 100% self-supply, show a need of about 2,500 GW RES in total, a storage capacity of about 240,000 GWh, corresponding to 6% of the annual energy demand, and a HVDC transmission grid of 375,000 GWkm. The combined cost for generation, storage and transmission excluding distribution, was estimated to be 6.87 ct/kWh.