Durations distribution of Rayleigh process with application to wind turbines

In the present paper, approximations to certain functions of the Rayleigh process distribution, beyond extreme thresholds, is derived. A close agreement between the results obtained and the corresponding results of the exact distributions confirms the validity of the present work. The derived approximations are implemented to analyze a real wind speed data and the results obtained are provided in this article. The behavior of a wind turbine (WT) is characterized by its power curve, which includes two extreme points: cut-in wind speed and cut-out wind speed. Therefore, accurate prediction of wind speed durations beyond these two thresholds will enable engineers to acquire several probabilistic statements such as the availability of electric power generation. These findings will be beneficial to design an efficient and reliable wind energy conversion system.