Modeling the hourly solar diffuse fraction in Taiwan

Using the data for global and diffuse radiation in Tainan, Taiwan, for the years of 2011 and 2012, respectively, four correlation models with five predictors: the hourly clearness index (kt), solar altitude, apparent solar time, daily clearness index and a measure of persistence of global radiation level, are constructed to relate the hourly diffuse fraction on a horizontal surface (d) to the clearness index. Two models use a single logistic equation for all kt values, Eqs. (6) and (7), and the other two models use a set of piece-wise linear equations for four kt intervals, Eqs. (8) and (9). The proposed models are compared respectively with the fourteen models available in the literature, in terms of the four statistical indicators: the mean bias error, the root-mean-square error, the t-statistic and the Bayesian Information Criterion, using the out-of-sample dataset for Tainan, Taiwan. It is concluded from the analysis that the proposed piece-wise linear models perform well in predicting the diffuse fraction, while the performances of the proposed logistic models are more case-dependent. Among those fourteen models considered in this study, the models developed by Erbs et al., Chandrasekaran and Kumar, and Boland et al. have competitive performances as the proposed piece-wise linear models do, when applying to the prediction of diffuse fraction in Tainan, Taiwan.