Storage has many benefits for power systems with a high share of renewable energy. It reduces renewable curtailment, can participate in ancillary services and contributes to system adequacy. However, its business model is far from clear since most of its revenues come from arbitrage in energy markets, and this is usually not enough to recover the investment. Advanced storage can facilitate the profitability of storage and ease the integration of renewables in power systems by reducing costs and allowing an enhanced performance. The profitability requirements of future advanced storage systems (batteries) are assessed in this paper by means of an optimization method and an uncertainty analysis for an optimal Iberian (Spain and Portugal) power system that meets the targets of their National Energy and Climate Plans. Results show that needed storage capacity is only a small part of the demanded energy, but technical advances are required for optimal performance. High prospective storage cost leads to a wind-dominated renewable mix, while low storage cost favours photovoltaics. Arbitrage with storage may cover its investment costs under carbon prices close to the actual Social Cost of Carbon.