Prospective power supply systems based on Renewable Energy Sources require measures to balance power generation and load at all times. The utilisation of storage devices and backup power plants is widely suggested for this purpose, whereas the best combination is still to be found. In this work, we present a modelling approach to systematically study scenarios of future power supply systems with a high share of electricity originating from wind and solar resources. By considering backup as a subordinate source of electricity with energy-only costs, the approach is independent of the actual full-load hours of the backup power plants. Applying the approach to multi-year meteorological data for Germany, cost-optimised combinations of storage devices and backup power are identified. We find that even in scenarios with significant excess generation capacities there is a need for storage devices or backup power plants with discharging power on the same order as the average load to balance the system at all times. Furthermore, these capacities seem to be required in some years of the multi-year period only. Our results imply that the societal need of having electricity available at all times can likely be satisfied by installing over-capacities only, whereas a balance has to be found between installing additional backup or storage or generation capacities.