Root-Transformed Local Linear Regression for Solar Irradiance Probability Density Estimation

Abstract

Solar energy is one of the most important and widely utilized renewable energy resource. Despite the many attractive features of solar-based renewables, the wide scale integration of solar generation into electric power systems presents significant challenges to network planners and operators, mainly due to the intermittent nature of solar energy. Most published work in this area is, however, focused on short-term forecasting studies used for unit commitment and energy market decisions with very little attention paid to solar irradiance probability density estimation needed for network planning and design studies. In this paper, a reliable nonparametric model of solar irradiance probability density is proposed based on the application of local linear regression in tandem with a root transformation method, introduced here for the first time. The performance of the proposed estimator is assessed via comparisons with the parametric Beta distribution (conventionally employed to model solar irradiance probability density) and two nonparametric kernel density estimation models; using the Kolmogorov–Smirnov (K–S) goodness-of-fit test, coefficient of determination ( $R^2$ ), and a number of error metrics. Results confirm the suitability and accuracy of the proposed method for solar irradiance probability density estimation.