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Modeling the hourly solar diffuse fraction in Taiwan
Affiliation:1. Energy Research Center, National Cheng Kung University, Tainan, Taiwan;2. Department of Aeronautics & Astronautics, National Cheng Kung University, Tainan, Taiwan;1. GECAD, Knowledge Engineering and Decision Support Research Center, Polytechnic of Porto (IPP), R. Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal;2. Automation and Control Group, Technical University of Denmark (DTU), Elektrovej Build. 326, DK 2800 Kgs. Lyngby, Denmark;1. University of Alaska Anchorage, Anchorage, AK, USA;2. Mechanical Engineering Dept., Ohio University, Athens, OH, USA;3. Civil Engineering Dept., University of Alaska Anchorage, Anchorage, AK, USA;4. Electrical Engineering Dept., University of Alaska Anchorage, Anchorage, AK, USA;5. Mechanical Engineering Dept., University of Alaska Anchorage, Anchorage, AK, USA;1. UR: Micro Electro Thermal Systems-ENIS, IPEIS, University of Sfax, B.P: 1172-3018 Sfax, Tunisia;2. LASMAP, Polytechnic Engineering School of Tunis, University of Carthage, La Marsa, Tunis, Tunisia;1. Institut UTINAM UMR CNRS 6213, Université de Franche-Comté, UFR Sciences et Techniques, 16 Route de Gray, 25030 Besançon Cédex, France;2. Solaronix SA, 129, rue de l''Ouriette, 1170 Aubonne, Switzerland
Abstract: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), (7), and the other two models use a set of piece-wise linear equations for four kt intervals, Eqs. (8), (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.
Keywords:Diffuse fraction  Multiple regression  Model assessment  Mathematical modeling
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