Investigation of Different Probability Distribution Functions for Wind Speed Modelling Using Classical and Novel Metaheuristic Methods

Abstract

This paper presents four different probability distribution functions (PDF) which can represent the stochastic nature of wind speed in a certain location. The four distributions are Weibull distribution, lognormal distribution, Gamma distribution, and inverse Gaussian distribution. The wind speed data utilized in this study is hourly average wind speed data collected from a wind farm in Texas city in the United States for five years. Two methods are used to get parameters of the abovementioned distributions, where the first one is a numerical method called the maximum likelihood method and the second one is a novel artificial intelligence method developed in 2021 called Aquila Optimizer. Histogram bars and the probability density function for the four probability distribution functions are presented to visualize the fitting of each graph. All probability distribution functions are compared using actual wind readings obtained from site and data obtained from distribution curve by correlation coefficient (R2), root means square error (RMSE), and Chi-square (X2). The Gamma distribution function gives the best fitting curve, which proves that not always Weibull is the best choice to represent wind speed distribution but selecting of PDF depends on wind speed data under study.