Gaussian Mixture Model for Estimating Solar Irradiance Probability Density

The increasing penetration of photovoltaic generation resources make it imperative for power network designers to assess the available resources by obtaining accurate estimates of solar irradiance at a given site/geographical area. The parametric Beta distribution has long been a popular choice in such studies; however, the use of parametric functions for probability density estimation (such as the Beta distribution) can be problematic and may lead to model mis-specification. The Gaussian Mixture Model (GMM) is proposed in this paper to provide a more robust estimation of solar irradiance probability density at a certain site. Multi-year solar data from eight locations in the United States is utilized to evaluate the accuracy of the GMM estimate and compare its performance with the popular Beta distribution. Assessments are carried out using three standard measures of error, coefficient of determination, and the Kolmogorov-Smirnov goodness-of-fit test for distributional adequacy. Results demonstrate that the GMM estimate produces a more robust estimation with better performance metrics when compared with the Beta distribution.