Extensive Numerical Analysis of PDF Parameters for Wind Energy in Brazil: A Study Across 27 Cities for 60 Years Wind Speed

This research conducts a comprehensive numerical assessment of wind energy potential across Brazil, leveraging six decades of wind speed data collected from 27 cities to analyze Probability Density Function (PDF) parameters and enhance wind resource mapping. The study employs the Weibull distribution, defined by its shape factor <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> and scale factor <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i>, to represent variations in wind speed. A total of nine numerical practices and methods including the Maximum Likelihood Method (MLM), Method of Moments (MM), Empirical Method (EM), Standard Deviation Method (STDM), Modified Maximum Likelihood Method (MMLM), Second Modified Maximum Likelihood Method (SMMLM), Graphical Method (GM), Least Mean Square Method (LSM), and Energy Pattern Factor Method (EPF) were utilized to achieve optimal parameter estimation. Statistical analysis was performed using various metrics such as the Index of Agreement (IA), Root Mean Square Error (RMSE), Chi-square test (𝜒<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>), Mean Absolute Percentage Error (MAPE), and Relative Root Mean Square Error (RRMSE). The findings indicated that MLM was the most precise method, followed by STDM, EM, MM, and EPF, while GM and LSM demonstrated lower effectiveness. The analysis determined a scale factor range of 2.17-2.36 m/s and a shape factor of 2.5-2.78, resulting in a bell-shaped Gaussian PDF. The Mean Wind Speed (MWS) was recorded at 2.06 m/s, which, despite being categorized as low, indicates the potential for effective deployment of small-scale wind turbines for energy production. This study offers significant insights for wind energy development in Brazil, presenting a methodological approach for optimizing the placement of wind turbines and minimizing electricity generation costs.