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, utilizing 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, characterized by shape factor k and scale factor c, to represent wind speed variations. Nine numerical methods, including 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 used for parameter estimation. Statistical analysis was conducted using metrics such as Index of Agreement (IA), Root Mean Square Error (RMSE), Chi-square test ( $\chi 2$ ), Mean Absolute Percentage Error (MAPE), and Relative Root Mean Square Error (RRMSE. The results showed that MLM was the most accurate method, followed by STDM, EM, MM, and EPF, while GM and LSM were less effective. The analysis revealed a scale factor range of 2.17-2.36 m/s and a shape factor of 2.5-2.78, indicating a bell-shaped Gaussian PDF. The Mean Wind Speed (MWS) was 2.06 m/s, suggesting potential for small-scale wind turbine deployment for energy production. This study provides valuable insights for wind energy development in Brazil, offering a methodological approach to optimize wind turbine placement and reduce electricity generation costs.