Fitting wind speed and wind direction probability distribution using mixture B-spline function

Abstract

Fitting wind speed and wind direction probability distribution is a crucial and fundamental task for the investigation of wind resource. This paper proposes a mixture basis(B)-spline function to fit wind speed and wind direction probability distribution. Such mixture B-spline function requires no prior assumption and eliminates the influence of subjective experience. A procedure has been developed that combines a binary genetic algorithm, maximum likelihood estimation, and a chi-squared test. This procedure can enable mixture B-spline function to adapt to various probabilistic behaviors. The wind speed and wind direction probability distributions of four North Dakota, U.S. sites are fitted by the mixture B-spline function and other five methods. Their goodness-of-fits are examined by chi-squared tests. The results indicate that the mixture B-spline function passes all the chi-squared tests and presents the highest goodness-of-fit. Additionally, the mixture B-spline function is used to calculate the mean wind power density, which can help identify sites with richer wind resources.