Fitting the wind speed probability distribution with Maxwell and power Maxwell distributions: A case study of North Dakota sites

Abstract

Fitting the wind speed probability distribution is essential to investigation of the wind energy potential and simulation of a wind farm. In this paper, Maxwell and power Maxwell distribution are newly introduced to fit the wind speed probability distribution of North Dakota sites. Parameter estimation for Maxwell and power Maxwell distributions is conducted with the maximum likelihood estimation method, method of moments, and least square method. Sampling procedures for these two distributions is developed with the linear interpolation approach. The applicability of the two distributions is justified by fitting wind speed samples recorded at twelve representative sites in North Dakota, United States. A detailed comparison of the two distributions and Rayleigh, Weibull, Lognormal, inverse Gaussian distributions is conducted. The comparison suggests that the power Maxwell distribution outperforms the Weibull distribution at most sites in terms of the fitting performance and modeling wind speed statistics. A suitable site for wind farm installation is identified. The performance of three parameter estimation methods is compared. The accuracy of developed sampling procedures is validated by taking differently sized samples of wind speeds from the power Maxwell distribution.