On the derivation of an analytical expression for wind power probability distribution function and capacity factor of turbine

It is shown here that if the PDF (Probability Distribution Function) of wind speed is a Rayleigh distribution with parameter [Formula: see text], then the PDF of wind power is a Weibull distribution with parameters [Formula: see text], where [Formula: see text] is the air density; if the wind speed PDF is a Weibull distribution with parameters [Formula: see text], then the wind power PDF is also a Weibull distribution with parameters [Formula: see text]; if the PDF of wind speed is a log-normal distribution with parameters [Formula: see text], then the PDF of wind power is also a log-normal distribution with parameters [Formula: see text]. The derived relationships allow us to quickly estimate parameters that indicate the wind power potential of the considered site, and the amount of wind energy generated by the turbine.