Energy storage applications are explored from a prosumer (consumers with generation) perspective for the island of Madeira in Portugal. These applications could also be relevant to other power networks. We formulate a convex co-optimization problem for performing arbitrage under zero feed-in tariff, increasing self-sufficiency by increasing self-consumption of locally generated renewable energy, provide peak shaving and act as a backup power source during anticipated and scheduled power outages. Using real data from Madeira we perform short and long time-scale simulations in order to select end-user contract which maximizes their gains considering storage degradation based on operational cycles. We observe energy storage ramping capability decides peak shaving potential, fast ramping batteries can significantly reduce peak demand charge. The numerical experiment indicates that storage providing backup does not significantly reduce gains performing arbitrage and peak demand shaving. Furthermore, we also use AutoRegressive Moving Average (ARMA) forecasting along with Model Predictive Control (MPC) for real-time implementation of the proposed optimization problem in the presence of uncertainty.