The output of renewable energy fluctuates significantly depending on weather conditions. In this work, unit commitment model is developed using the forward dynamic programming approach, to analyze the effect of integrating wind energy on the power generation system operation. The model obtains the time series for the operational state of generators that would maximize the profits of an electric power utility by taking into account both the forecast of output for the wind energy as well as the demand response of consumers. In this work, the case study of the island of Corvo in the Portuguese archipelago Azores is considered. This system consists of diesel generators with a plan to integrate wind energy into the system as well implement a Demand Response strategy to utilise the wind energy during hours of excess. The study suggests a power generation schedule for the existing power system on the island in order to lower the cost of operation. The viability of integrating wind energy was also confirmed and a generation schedule was produced. A demand response strategy was integrated into the model, using the water heating demand as a shiftable load. The water heater load-shifting was carried out using a real-time-pricing strategy to incentivize the utilization of electricity during hours of excess wind production. Several scenarios were studied and the impact of the demand response strategy was found to be significant. Finally, the effect of limiting the instantaneous wind penetration was studied. It was found that the total wind penetration is affected significantly by the restrictions on the instantaneous wind penetration only during days of high average wind speeds.