Journal of Applied Mathematics and Physics

Volume 7, Issue 12 (December 2019)

ISSN Print: 2327-4352   ISSN Online: 2327-4379

Google-based Impact Factor: 1.00  Citations  

Investigations into Some Simple Expressions of the Gamma Function in Wind Power Theoretical Estimate by the Weibull Distribution

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DOI: 10.4236/jamp.2019.712209    765 Downloads   2,656 Views  Citations
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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 < v >, the variance of v around < v > 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 < v >, the variance σ2 of the wind speed v; around the mean speed and the average wind power density.

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Touré, S. (2019) Investigations into Some Simple Expressions of the Gamma Function in Wind Power Theoretical Estimate by the Weibull Distribution. Journal of Applied Mathematics and Physics, 7, 2990-3002. doi: 10.4236/jamp.2019.712209.

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