ISSN: 2375-3927
International Journal of Mathematical Analysis and Applications  
Manuscript Information
Improved Mathematical Modeling of the Hourly Solar Diffuse Fraction (HSDF) - Adrar, Algeria Case Study
International Journal of Mathematical Analysis and Applications
Vol.4 , No. 2, Publication Date: Jul. 5, 2017, Page: 8-12
523 Views Since July 5, 2017, 317 Downloads Since Jul. 5, 2017

Nadjem Bailek, Department of Physics, Faculty of Science, University Djilali Liabes of Sidi Bel-Abbes, Sidi Bel-Abbes, Algeria.


Kada Bouchouicha, Research Unit in Renewable Energies in Saharan Medium (URER.MS), Renewable Energies Development Center (CDER), Bouzaréah, Algeria.


Mohamed EL-Shimy, Electrical Power and Machines Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt.


Abdeldjalil Slimani, Research Unit in Renewable Energies in Saharan Medium (URER.MS), Renewable Energies Development Center (CDER), Bouzaréah, Algeria.


Keh-Chin Chang, Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan.


Abdalhe Djaafari, Department of Physics, Faculty of Science, University of Tamanghasset, Tamanghasset, Algeria.


Solar energy is among the excellent alternative energy resources; however, it suffers from significant problems. These problems are mainly due to the inherent variability, and intermittency of the solar resource; however, proper predictability of the resource can reduce the consequent impacts of the mentioned problems. Enhancing the predictability of the solar resource provides an essential tool for the design, performance analysis, and economic evaluation of various solar energy projects. In this paper, highly accurate mathematical models for estimating the hourly diffuse solar fraction are presented for enhancing the predictability of the solar resource over Adrar, Algeria big south desert. The presented modeling is based on clearance index measurements. The best found model for the considered site is found to be the sigmoid logistic empirical model. This model shows the highest accuracy in comparison with other models where its correlation coefficient (R), and the Nash-Sutcliffe NSE are found to be 93.7% and 84.2% respectively. In addition, the segmoid logistic model shows very low values of the mean bias error (MBE), and root mean square error (RMSE).


Solar Diffuse Fraction, Multiple Regression, Mathematical Modeling


Olmo, F., et al., Prediction of global irradiance on inclined surfaces from horizontal global irradiance. Energy, 1999. 24(8): p. 689-704.


Kuo, C.-W., W.-C. Chang, and K.-C. Chang, Modeling the hourly solar diffuse fraction in Taiwan. Renewable Energy, 2014. 66: p. 56-61.


Kuo, C.-W. and K.-C. Chang, In-situ measurements of solar diffuse fraction in southern Taiwan. Journal of the Chinese Institute of Engineers, 2015. 38(6): p. 723-730.


Liu, B. Y. and R. C. Jordan, The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar energy, 1960. 4(3): p. 1-19.


Reindl, D. T., W. A. Beckman, and J. A. Duffie, Diffuse fraction correlations. Solar energy, 1990. 45(1): p. 1-7.


Khalil, S. A. and A. Shaffie, A comparative study of total, direct and diffuse solar irradiance by using different models on horizontal and inclined surfaces for Cairo, Egypt. Renewable and Sustainable Energy Reviews, 2013. 27: p. 853-863.


Bugler, J., The determination of hourly insolation on an inclined plane using a diffuse irradiance model based on hourly measured global horizontal insolation. Solar Energy, 1977. 19(5): p. 477-491.


Karatasou, S., M. Santamouris, and V. Geros, Analysis of experimental data on diffuse solar radiation in Athens, Greece, for building applications. International journal of sustainable energy, 2003. 23(1-2): p. 1-11.


Orgill, J. and K. Hollands, Correlation equation for hourly diffuse radiation on a horizontal surface. Solar energy, 1977. 19(4): p. 357-359.


Hawlader, M., Diffuse, global and extra-terrestrial solar radiation for Singapore. International journal of ambient energy, 1984. 5(1): p. 31-38.


De Miguel, A., et al., Diffuse solar irradiation model evaluation in the north Mediterranean belt area. Solar Energy, 2001. 70(2): p. 143-153.


Chandrasekaran, J. and S. Kumar, Hourly diffuse fraction correlation at a tropical location. Solar Energy, 1994. 53(6): p. 505-510.


Jacovides, C., et al., Comparative study of various correlations in estimating hourly diffuse fraction of global solar radiation. Renewable Energy, 2006. 31(15): p. 2492-2504.


Boland, J., L. Scott, and M. Luther, Modelling the diffuse fraction of global solar radiation on a horizontal surface. Environmetrics, 2001. 12(2): p. 103-116.


Boland, J., B. Ridley, and B. Brown, Models of diffuse solar radiation. Renewable Energy, 2008. 33(4): p. 575-584.


Marques Filho, E. P., et al., Global, diffuse and direct solar radiation at the surface in the city of Rio de Janeiro: Observational characterization and empirical modeling. Renewable Energy, 2016. 91: p. 64-74.


Bouchouicha, K. and B. Oulimar, La chaine de mesure radiométrique à l’Unité de Recherche en Energie Renouvelable en Milieu Saharien d’Adrar. International Conference on Energy and Sustainable Developmenticesd’13, Adrar - Algeria 19-20 February 2013, 2013. 2.


Long, C. and Y. Shi, An automated quality assessment and control algorithm for surface radiation measurements. Open Atmos. Sci. J, 2008. 2(1): p. 23-37.


Gueymard, C. A. and J. A. Ruiz-Arias, Extensive worldwide validation and climate sensitivity analysis of direct irradiance predictions from 1-min global irradiance. Solar Energy, 2016. 128: p. 1-30.


Sonmete, M. H., et al., Assessing monthly average solar radiation models: a comparative case study in Turkey. Environmental monitoring and assessment, 2011. 175(1-4): p. 251-277.


Despotovic, M., et al., Evaluation of empirical models for predicting monthly mean horizontal diffuse solar radiation. Renewable and Sustainable Energy Reviews, 2016. 56: p. 246-260.


Mohammadi, K., et al., Influence of introducing various meteorological parameters to the Angström–Prescott model for estimation of global solar radiation. Environmental Earth Sciences, 2016. 75(3): p. 1-12.


Namrata, K., S. Sharma, and S. Seksena, Empirical models for the estimation of global solar radiation with sunshine hours on horizontal surface for Jharkhand (India). Applied Solar Energy, 2016. 52(3): p. 164-172.


Hassan, G. E., et al., New temperature-based models for predicting global solar radiation. Applied Energy, 2016. 179: p. 437-450.


Abdo, T. and M. EL-Shimy, Estimating the global solar radiation for solar energy projects–Egypt case study. International Journal of Sustainable Energy, 2013. 32(6): p. 682-712.

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