The Azores Regional Government, through the Sustainable Energy Action Plan for the Azorean Islands, assumed that by the year 2018, 60% of electricity would be generated from renewable energy sources. Nevertheless, by increasing renewable energy sources share in the electricity mix, peak energy that exceeds grid capacity cannot be used unless when considering energy storage systems. Therefore, this article aims at determining, among batteries and Pumped Hydro Systems, the most cost-effective energy storage system to deploy in Terceira Island, along with geothermal, wind, thermal and bio waste energy, while considering demand and supply constraints. It is concluded that a pumped hydro system sited in Serra do Morião-Nasce Água is the best option for storage of the excess generated energy when compared with batteries. However, further studies should analyze environmental constraints. It is demonstrated that by increasing the storage power capacity, a pumped hydro system improves its cost efficiency when compared with batteries. It is also demonstrated that, to ensure quality, economic feasibility, reliability and a reduction of external costs, it is preferable to replace fuel-oil by wind to generate electricity up to a conceivable technical limit, while building a pumped hydro system, or dumping the excess peak energy generated.