Comparison of Weibull and Gaussian Mixture Models for Wind Speed Data Analysis

Abstract

In order to have a reliable estimate of wind energy potential of a site, high frequency wind speed and direction data recorded for an extended period of time is required. Weibull distribution function is commonly used to approximate the recorded data distribution for estimation of wind energy. In the present study a comparison of Weibull function and Gaussian mixture model (GMM) as theoretical functions are used. The data set used for the study consists of hourly wind speeds and wind directions of 54 years duration recorded at Ijmuiden wind site located in north of Holland. The entire hourly data set of 54 years is reduced to 12 sets of hourly averaged data corresponding to 12 months. Authenticity of data is assessed by computing descriptive statistics on the entire data set without average and on monthly 12 data sets. Additionally, descriptive statistics show that wind speeds are positively skewed and most of the wind data points are observed to be blowing in south-west direction. Cumulative distribution and probability density function for all data sets are determined for both Weibull function and GMM. Wind power densities on monthly as well as for the entire set are determined from both models using probability density functions of Weibull function and GMM. In order to assess the goodness-of-fit of the fitted Weibull function and GMM, coefficient of determination (R2) and Kolmogorov-Smirnov (K-S) tests are also determined. Although R2 test values for Weibull function are much closer to ‘1’ compared to its values for GMM. Nevertheless, overall performance of GMM is superior to Weibull function in terms of estimated wind power densities using GMM which are in good agreement with the power densities estimated using wind data for the same duration. It is reported that wind power densities for the entire wind data set are 307 W/m2 and 403.96 W/m2 estimated using GMM and Weibull function, respectively.