Unbiased cross-validation kernel density estimation for wind and PV probabilistic modelling

Abstract

Uncertainties associated with power generation from wind energy systems and Photovoltaic (PV) power systems present a major challenge for power system planners and operators. To account for such uncertainties, probabilistic models and probability density estimations for wind speed and solar irradiance, and their corresponding wind and PV power are highly required for long-term (multi-year) power system planning, expansion, and dispatching tools. In this article, a novel Kernel Density Estimator (KDE) model using unbiased cross-validation method for bandwidth selection is proposed for the estimation of both wind speed and solar irradiance probability densities. The estimation performance of the proposed model is assessed against the traditional parametric models (Weibull and Rayleigh distributions for wind speed, and Beta distribution for solar irradiance), and the traditional nonparametric KDE approach employing a rule-of-thumb method for bandwidth selection. The performance accuracy of all models is tested using the coefficient of determination R2, two error metrics (Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE)), in addition to the Kolmogorov–Smirnov (K–S) test that was used to assess the goodness-of-fit. The proposed approach achieved the highest percentage improvements for R2 (24% and 23%), and the lowest MAE (66% and 36%) and RMSE (63% and 25%) metrics over the popular parametric distributions for wind speed and solar irradiance, respectively, in addition to the K–S test p-values indicating a clear evidence of a good fit. Results confirm the accuracy and robustness of the probability density estimates for wind speed and solar irradiance produced by the proposed model.