Abstract
The Weibull distribution is a probability density function (PDF) which is widely used in the study of meteorological data. The statistical analysis of the wind speed v by using the Weibull distribution leads to the estimate of the mean wind speed , the variance of v around and the mean power density in the wind. The gamma function Γ is involved in those calculations, particularly Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k). The paper reports the use of the Weibull PDF f(v) to estimate the gamma function. The study was performed by looking for the wind speeds related to the maximum values of f(v), v2 f(v) and v3 f(v). As a result, some approximate relationships were obtained for Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k), that use some fitting polynomial functions. Very good agreements were found between the exact and the estimated values of Γ (1+n/k) that can be used for the estimation of the mean wind speed , the variance σ2 of the wind speed v; around the mean speed and the average wind power density.
Highlights
A growing interest in renewable sources of energy is observed, owing to the increase in electricity demand and the world environmental concern
The Weibull distribution is a probability density function (PDF) which is widely used in the study of meteorological data
Very good agreements were found between the exact and the estimated values of Γ (1+ n k ) that can be used for the estimation of the mean wind speed v, the variance σ2 of the wind speed v around the mean speed and the average wind power density
Summary
A growing interest in renewable sources of energy is observed, owing to the increase in electricity demand and the world environmental concern. Several probability density functions (PDF) are used in the study of meteorological data, such as the. 2-parameter Weibull distribution, the 3-parameter Weibull distribution or the mixture Weibull distribution which are widely used in wind energy potential analysis. This Weibull model is often used for the assessments of the mean wind speed and the mean power density. The beta PDF is used in the study of meteorological data All those PDF calculations use the gamma function. The objective of the present work is to find some simple expressions of the gamma function, linked to a fitting parameter of the Weibull PDF, which may be used in wind power estimate and in the study of other meteorological data
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