Tail-Weighted Wind Speed Distribution by Mixture Model with Constrained Maximum Likelihood

Abstract

In order to reduce the estimation uncertainty for the wind energy output, the accurate assessment of the wind speed distribution plays an important role. Due to the influence of the complex terrain, the wind speed data in mountainous area may show the heavy tail. The tail has an important effect on the annual energy production of the wind turbine because of the power output being the cubic of the wind speed. Hence the heavy tail should be highlighted before choosing the proper distributions. To characterize the heavy tail, the box plot, QQ plot and conditional mean exceedance are used. In addition, the wind climate in the mountainous area is very complicated and typically mixed by local storms and large-scale wind flows. The distribution of the wind speed is prone to exhibit bimodal or even multi-modal nature. The conventional unimodal distributions such as Weibull may not well portray these distributions. The mixture distribution has more flexibilities to handle this challenge. Both generalized extreme value distribution and generalized Pareto distribution are considered to formulate the mixture distribution in modeling the tail. The maximum likelihood method and the constrained maximum likelihood method are used to estimate distribution parameters. The comprehensive evaluation criteria are adopted to determine the most appropriate distribution of four sets of wind speed in the mountainous area of Yunnan, China. Graphical tools, such as histogram density curve and QQ plot, are also used for evaluation. Results show that heavy tail distribution should be considered for the wind data in mountainous areas and the proposed mixture model with the constrained maximum likelihood method for the parameter estimation will be superior for the wind energy potential estimation.