Wind has become a popular renewable energy resource in the last two decades. Wind speed modeling is a crucial task for investors to estimate the energy potential of a region. The aim of this paper was to compare the popular unimodal wind speed distributions with their two-component mixture forms. Accordingly, Weibull, gamma, normal, lognormal distributions, and their two-component mixture forms; two-component mixture Weibull, two-component mixture gamma, two-component mixture normal, and two-component mixture lognormal distributions were employed to model wind speed datasets obtained from Belen Wind Power Plant and Gökçeada Meteorological Station. This paper also provides the comparison of gradient-based and gradient-free optimization algorithms for maximum likelihood (ML) estimators of the selected wind speed distributions. ML estimators of the distributions were obtained by using Newton-Raphson, Broyden-Fletcher-Goldfarb-Shanno, Nelder-Mead, and simulated annealing algorithms. Fit performances were compared based on Kolmogorov-Smirnov test, root mean square error, coefficient of determination (R 2), and power density error criteria. Results reveal that two-component mixture wind speed distributions have superiority over the unimodal wind speed distributions.

Renewable energy has become a prominent subject for researchers since fossil fuel reserves have been decreasing and are not promising to meet the energy demand of the future. Wind takes an important place in renewable energy resources and there is extensive research on wind speed modeling. Herein, one of the most commonly used distributions for wind speed modeling is the Weibull distribution with its simplicity and flexibility. Maximum likelihood (ML) method is the most frequently used technique in Weibull parameter estimation. Iterative techniques such as Newton-Raphson (NR) use random initial values to obtain the ML estimators of the parameters of the Weibull distribution. Therefore, the success of the iterative techniques highly depends on the initial value selection. In order to deliver a solution to the initial value problem, genetic algorithm (GA) is considered to obtain the estimators of the model parameters. The ML estimators obtained using the GA and NR techniques are compared with the method of moments (MoM) estimators via Monte Carlo simulation and wind speed applications. The results show that the ML estimators obtained using GA present superiority over MoM and the ML estimators obtained using NR.

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