Aplicação de algoritmos de otimização metaheurísticos na estimativa dos parâmetros ótimos de diferentes distribuições de velocidade do vento em duas cidades do nordeste brasileiro

Abstract

For a better use of wind energy, a thorough analysis of the wind resource is essential. In this analysis, wind speed distributions play an important role, the most common being the Weibull distribution. However, this distribution is not always the most suitable, which makes it necessary to evaluate different distributions to obtain more reliable information. Another essential step is the estimation of the parameters governing these distributions, as the accuracy of these estimates directly affects the power generation calculations. In the last years, different optimization methods have been used for this purpose and, compared to traditional numerical methods, they have performed better. However, in wind energy, the application of these methods is centered on the conventional two-parameters distributions, such as Weibull, Gamma and Lognormal. Moreover, different authors emphasize the lack of studies that use optimization methods for this purpose. Given this scenario, four metaheuristic optimization algorithms (MOA), namely, Migrating Birds, Imperialist Competition, Harmony Search and Cuckoo Search, were used in this study to fit 11 wind speed distributions. The study was conducted in two cities in Northeastern Brazil, which is one of the best regions in the world for wind energy generation, since winds are favorable for this purpose. Three distinct objective functions were also analyzed to determine which one should be applied to the MOA in order to obtain a better fit. Finally, the fits obtained by the MOA were compared, through an objective statistical analysis, with those obtained by the Maximum Likelihood (MLE) numerical method. The objective function that achieved best results was the maximization of the determination coefficient. Regarding the MLE, the MOA presented significantly better fits, since the Global Score (GS) values obtained were lower. This demonstrates the ability of MOA to accurately estimate the parameters of the distribution models. In both analyzed regions, the three-parameter models generally provided better fit than the two-parameter models. In São João do Cariri, the best fit was obtained through the Generalized Gamma distribution, which presented GS = 0; 005766, and the widely used Weibull distribution ranked fourth with GS = 0; 009369. In Petrolina, the best fit was obtained through the Extended Generalized Lindley distribution, which presented GS = 0; 005246, and the Weibull distribution ranked fifth with GS = 0; 007894. Birnbaum-Saunders and Lognormal models presented the worst fits in both regions.