Performance evaluation of Weibull analytical methods using several empirical methods for predicting wind speed distribution

Abstract

ABSTRACT The Weibull distribution function with shape (k) and scale (c) parameters predicts wind speed distribution for different locations. The k and c parameters have been estimated by using several analytical methods, but it provides different results in the same wind speed distribution data. In this work, the correlation technique was applied to evaluate the performance of analytical methods using several empirical methods. The analytical methods presented including Method of Moments (MoM), Energy Pattern Density (EPD), Graphic Method (GM), and Maximum Likelihood Estimator (MLE). Five empirical methods were evaluated graphically by using the GM method to estimate the Weibull two-parameter. The Weibull two-parameter of correlation coefficient (r) of greater than 0.9503 indicated from four empirical methods. Again, five empirical methods for k parameter and four empirical methods for c parameter were used in the special case of MoM and EPD methods. The results indicated four empirical methods for estimating k parameter and two empirical methods for estimating c parameter having the r of greater than 0.7. When empirical methods of k and c parameter correlated, six matching patterns were identified from 20 possible pairs. Comparison of GM, MLE, and selected pairs of k and c values predicted from empirical methods resulted from MoM and EPD indicated the average coefficient of best-fit of 0.8851 and root-mean-square-error of 0.2083. Therefore, the use of more than one empirical method in one analytical method of MoM, EPD, and GM would improve the prediction of Weibull distribution.