We develop a dispatch and investment model to study the role of power storage and other flexibility options in a greenfield setting with high shares of renewables. The model captures multiple system values of power storage related to arbitrage, dispatchable capacity, and reserves. In a baseline scenario, we find that power storage requirements remain moderate up to a renewable share of around 80%, as other options on both the supply side and demand side also offer flexibility at low cost. Yet storage plays an important role in the provision of reserves. If the renewable share increases to 100%, the required capacities of power storage and other technologies increase strongly. As long-run parameter assumptions are highly uncertain, we carry out a range of sensitivity analyses, for example, with respect to the costs and availabilities of storage and renewables. A common finding of these sensitivities is that – under very high renewable shares – the storage requirement strongly depends on the costs and availability of other flexibility options, particularly on biomass availability. We conclude that power storage becomes an increasingly important element of a transition towards a fully renewable-based power system. Power storage gains further relevance if other potential sources of flexibility are less developed. Supporting the development of power storage should thus be considered a useful component of policies designed to safeguard the transition towards renewables.