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 s, then the PDF of wind power is a Weibull distribution with parameters a=2ρs3,b=23, where ρ is the air density; if the wind speed PDF is a Weibull distribution with parameters a,b, then the wind power PDF is also a Weibull distribution with parameters a3ρ2,b3; if the PDF of wind speed is a log-normal distribution with parameters μ,σ, then the PDF of wind power is also a log-normal distribution with parameters lnρ2+3μ,3σ. 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.