An extensive mathematical approach for wind speed evaluation using inverse Weibull distribution

Abstract

Wind velocity and potential are frequently estimated using probability density functions (PDFs) such as the Inverse Weibull and Rayleigh. Determining whether they are suitable for modelling observed distributions is crucial. Many wind energy systems require a thorough understanding of wind speed probability distributions. This research presents an extensive mathematical approach for wind speed evaluation using the inverse Weibull distribution (IWD) and a modified maximum likelihood function. IWD is a valuable tool for modelling wind speed characteristics, providing insights into the PDF and cumulative distribution function (CDF) of wind speeds. The suggested modified maximum likelihood (MML) function includes tweaks and improvements to increase parameter estimate accuracy in the IWD. The IWD is computed using the MML function, which considers data features, outliers, and unique research demands. Model calibration techniques, including goodness-of-fit assessment, sensitivity analysis, and error analysis, are employed to refine and assess the model’s accuracy. The developed mathematical model based on the inverse Weibull distribution and modified maximum likelihood function offers a robust approach for wind speed evaluation and analysis, contributing to renewable energy resource assessment, wind farm design, and structural engineering applications.

Keywords

• Inverse Weibull distribution
• Modified maximum likelihood
• Probability density functions
• Wind speed