Wind speed probability density estimation using root-transformed local linear regression

Abstract

Despite the many attractive features of wind-based renewables, the intermittency of wind generation stands out as a critical challenge. An accurate and reliable nonparametric wind speed probability density model is proposed in this paper based on the application of local linear regression in tandem with a root transformation method, introduced here for the first time. The proposed root-transformed local linear regression approach provides a robust estimate of wind speed distribution and produces more accurate results than kernel density estimation models. The performance of the root-transformed local linear regression estimator is assessed via comparisons with three popular parametric models (Rayleigh, Weibull and Gaussian distributions), two additional parametric models (Birnbaum–Saunders and Nakagami distributions) recently suggested for wind speed probability density estimation, and two nonparametric kernel density estimation models using two standard goodness-of-fit hypothesis tests (Chi-squared and Kolmogorov–Smirnov), coefficient of determination and two error metrics (root mean square error and mean absolute error). Results confirm the accuracy of the proposed root-transformed local linear regression estimator for modelling wind speed probability density, with substantial improvements in all error metrics over parametric and kernel density estimation models.