Solar Probability Density Estimation Using Adaptive Parametric/Nonparametric Hybrid Model

The accurate estimation of solar irradiance probability distribution is essential when assessing the level of available solar resources and attempting to minimize the effect of solar power variability on power system planning. The Beta distribution has long been a popular choice in power systems for modeling solar data. The use of parametric models, however, has been shown to be problematic and can lead to model mis-specification. This article proposes an adaptive hybrid model combining the Beta distribution with the Kernel Density Estimation (KDE) approach for solar irradiance probability density estimation, in which the weights of the two components of the hybrid model are adjusted using the least mean square algorithm to obtain the most appropriate combination. The hybrid model is evaluated using multi-year data at six different sites in the United States. The assessment is carried out using the Kolmogorov-Smirnov goodness-of-fit test, coefficient of determination ( $R^{2}$ ), and two error measures: Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). By combining parametric and nonparametric approaches, the adaptive model achieves a better fit and substantial improvements in all metrics when compared with the Beta distribution and other statistical models. The proposed hybrid estimator is the only model for which the null hypothesis is not rejected for all considered datasets. In terms of the statistical metrics, percentage improvements of up to 92.2% ( $R^{2}$ ), 30.6% (MAE), and 26.6% (RMSE) were achieved when compared with the Beta distribution results. Similarly, when compared with the threshold-based model, percentage improvements of up to 32.7% ( $R^{2}$ ), 20.6% (MAE), and 16.0% (RMSE) were obtained.