As future grids are becoming more decentralised, I study a stand-alone grid where the penetration of wind energy is high, and exploit a joint planning of energy storage and renewable energy source, as this can potentially result in a more economical and efficient energy system. More specifically, I consider an energy system that consists of a gas-fired plant and a small wind farm with a capacity for energy storage. I assume that the gas-fired plant has a maximum generation that is no more than the electricity consumption. I first propose an optimisation model with known wind speed and electricity demand. Then I gradually extend this deterministic model to study the stochastic nature of the wind speed and electricity demand forecasting. Numerical applications in two chosen locations with different characteristics have been provided for demonstration. In the model extension, I compare battery storage with the other storage technologies by modifying the part of the cost functional, charging/discharging capacity and efficiency rate corresponding to the storage. The optimal solution has changed due to different efficiencies, costs and charging/discharging capacities. Compressed air energy storage and pumped hydroelectric storage may have the advantage in cost, but if a big surplus of energy is needed to get charged within a short time period, batteries might be a better choice as flywheels are very expensive. Furthermore, I include carbon emission modelling from the gas-fired plant by applying a carbon tax and a carbon emission cap. In my system, for a carbon tax to have a similar effect in reducing emissions in comparison to a carbon emission cap, it would need to be very high. Finally, I consider the possibility of connecting my system to the National Grid where I import from, or export to, when my system has an electricity shortage or surplus in meeting the demand. The results provide helpful insights in planning a joint deployment of generation capacity and energy storage and show that the system operates more efficiently and economically when it is connected to the National Grid.