Gaussian Mixture Model for the Estimation of Multiyear Solar Irradiance Probability Density
Maisam Wahbah, Tarek H. M. EL-Fouly, Bashar Zahawi, Samuel F. Feng
Abstract
The increasing popularity of photovoltaic resources and the connection of solar farms in larger sizes to power distribution networks make it imperative for network designers to assess the variability of available solar resources at a given location. This is normally achieved by attempting to obtain an accurate estimation of the probability density function (pdf) of solar irradiance at the given site. The parametric beta distribution has long been a popular choice in such studies because of its ease of use. However, pdf estimation using parametric functions can lead to inaccurate models and suboptimal decisions being made about the suitability of potential farm site. In this article, a more robust estimation of solar irradiance pdf than that given by the popular beta distribution is obtained by using a Gaussian mixture model (GMM). Using multiyear solar data, the GMM estimate is also compared with a widely used nonparametric kernel density estimation model that employs a common rule-of-thumb bandwidth selection method. Assessments are carried out using a goodness-of-fit test, three error measures, and the coefficient of determination index. Results demonstrate the improved accuracy and robustness of the GMM, which consistently achieves better performance metrics compared with the kernel density estimation (KDE) model and the beta distribution.