This paper proposes a power-speed (P-V) model of the wind turbine by assuming three different functions for the first performance region; cubic, quadratic and uncorrected cubic. These three functions have been compared with the manufacturer models of five different wind turbines which were installed in five different locations in Jordan; Tafila, Hofa, Fujeij, Al Rajef, and Deahan. The wind turbine of these wind farms are considered as large scale HAWT in the range of Mw. The generated P-V models are developed by applying a new method described in this paper which is basically based on generating a multiplier factor x. In this study, the quadratic model shows the highest correlation compared with the other models. The wind energy yield for the selected wind farms has been estimated by a mathematical modelling based on Rayleigh distribution function, derived in this paper. The energy yield using this mathematical model has been compared with the measured energy output of four wind farms, Tafila, Hofa, Al Rajef, and Deahan. The measured energy were provided by the operators of these wind farms which are: Jordan Wind Project Company(JWPC), Central Electricity Generation Company (CEGC), Green Watts Renewable Energy (GWRC)and Korean Southern Power Company(KOSPO). Results show that the estimated energy using the quadratic wind turbine model for all wind farms are very close to the actual output. Accuracy analysis for the quadratic model resulted in an error of less than 10 % between the measured and estimated energy output for all wind farms. The capacity factors for the selected wind farms have been estimated using the quadratic P-V model. Results show that Tafila wind farm has the highest capacity factor which is around 47 % .