The present work is the investigation of a specific SWES. This system is designed to provide enough power for domestic use that satisfies a single household’s demand and allows a certain level of autonomy. The whole work is based on simulation. Models are elaborated to simulate the power source (wind turbine), a storage battery, the electrical load and the relevant meteorological conditions, in addition to other items that are needed to represent the SWES satisfactorily. MATLAB/SIMULINK software is used for the whole system simulation. Focus is put onto the power source and battery. The load situated in various climatic zones of Algeria is represented as a power demand that needs be satisfied. Finally, the economic analysis has resulted in the calculation of the installed total cost, kWh cost, and the actualized total cost for the wind energy source. The simulation results indicate that the coverage provided by the wind/battery system depends on the wind turbine nominal power. It depends also from the local wind speed distribution As far as the economic results are concerned, it appears that the cost of the energy produced by the wind/battery system is very high (1.3-4$/kWh) compared to those corresponding to conventional installations (0.4$/kWh). This, however, is not to be considered as a negative determinant factor since the local authorities plan to manufacture renewable energy equipment locally and, by doing so, cancel the effects of subsidizing the local fossil fuels on the imported machines costs, which will in turn be favorably reflected on renewable energy costs.