This paper presents a technical study for wind power systems in three sites in Kuwait namely Al-Wafra, Um-Omara and Al-Taweel. Hourly wind speed data for three years are used in order to optimally sizing the wind power systems. Firstly, the Wiebull, function is used to model the wind speed data for each sites. After that a numerical method is used to optimize the energy sources in the power system (wind turbine and battery) using MATLAB. After that the MATLAB is used to analyze the performance of these systems.  The results show that the sizing ratio of the turbine for Al-Wafra, Um-Omara and Al-Taweel are 17.61, 23.88 and 23.49 respectively. While the sizing ratio of the storage battery for Al-Wafra, Um-Omara and Al-Taweel are 0.724, 1.566 and 1.22 respectively. On the other hand the average cost of energy generated by wind power systems in Kuwait in case of standalone system is 0.282 USD/ kWh while it is 0.15 USD/kWh in case of grid connected system. This research presents worthwhile technical information for those who are interested in wind power systems installation in Kuwait.