Skip to main content
SpringerLink
Log in

The estimation of diffuse solar radiation on tilted surface using created new approaches with rational function modeling

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

In this study, polynomial function modeling and rational function modeling were used to create three new models for the estimation of diffuse solar radiation on a tilted surface, which is the most important and necessary parameter for solar energy systems. Solar radiation data used in the study were obtained from the Turkish State Meteorological Service. The new model, created using the rational function modeling for the first time, displayed a better performance than the models developed using polynomial function modeling in the literature. The performances of the models were compared by way of statistical parameters. The general validity of the models developed was tested against solar data for the Athens, Madrid, Berlin and Bucharest. Also, the optimum tilt angles were determined via diffuse solar radiation models. Annual optimum tilt angles for reference provinces, Tokat, Corum, Amasya and Yozgat were determined as 17°, 17°, 15° and 16°, respectively. The total gains were obtained on optimum tilt angles for the provinces of Tokat, Corum, Amasya and Yozgat were 46.5%, 56.21%, 39.37% and 44.49%, respectively. As a result, the proposed new model, based on rational function modeling for the estimation of diffuse solar radiation, displayed the best performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Abbreviations

H :

Monthly average daily global radiation on a horizontal surface (kJ/m2-day)

\( H_{\text{d}} \) :

Diffuse solar radiation (kJ/m2-day)

\( H_{0} \) :

Monthly average daily extraterrestrial radiation (kJ/m2-day)

\( H_{\text{b}} \) :

Beam solar radiation (kJ/m2-day)

\( K_{\text{T}} \) :

Monthly average clearness index

\( I_{\text{SC}} \) :

Solar constant (W/m2)

\( \varphi \) :

Latitude (°)

\( \delta \) :

Solar declination (°)

\( \omega_{\text{s}} \) :

Hour angle (°)

\( \omega_{\text{s}}^{\prime } \) :

Sunset hour angle (°)

n :

Day of the year

\( H_{\text{T}} \) :

Total solar radiation (kJ/m2)

R :

A ratio that is used to determine the daily average radiation on a tilted surface to that on a horizontal surface for each month

\( R_{\text{b}} \) :

Beam radiation conversion factor

\( \rho \) :

Ground reflectance

\( s \) :

Tilt angle (°)

\( S_{\text{opt}} \) :

Optimum tilt angle (°)

RMSE:

Root-mean-square error

R 2 :

Determination coefficient

Adj-R2 :

Adjusted coefficient of determination

SSE:

Sum of squares error

PVs:

Photovoltaics

IMD:

Indian Meteorological Department

EAR:

Eastern Anatolia Region

MBE:

Mean bias error

MPE:

Main percentage error

NASA:

National Aeronautics and Space Administration

References

  1. Initiative GE. Global electricity initiative executive summary GEI2014 (2014)

  2. Y Kuang, Y Zhang, B Zhou, C Li, Y. Cao, L. Li, et al. Renew. Sustain. Energy Rev. 59 504 (2016)

    Google Scholar 

  3. S Sinha and S S Chandel Renew. Sustain. Energy Rev. 50 755 (2015)

    Google Scholar 

  4. O Gunay, A H Yavuz and R Ahiska Int. J. Hydrog. Energy 42 8310 (2017)

    Google Scholar 

  5. G Wu, Y Liu and T Wang Energy Convers. Manag. 48 2447 (2007)

    Google Scholar 

  6. C Ekici and I Teke Results Phys. 9 263 (2018)

    ADS  Google Scholar 

  7. S Janjai, P Pankaew and J Laksanaboonsong Appl. Energy 86 1450 (2009)

    Google Scholar 

  8. S Chandel, R Aggarwal and A Pandey J. Sol. Energy Eng. 127 417 (2005)

    Google Scholar 

  9. A Das, J K Park and J H Park J. Atmos. Solar Terr. Phys. 134 22 (2015)

    ADS  Google Scholar 

  10. A El-Sebaii, F Al-Hazmi, A Al-Ghamdi and S J Yaghmour Appl. Energy 87 568 (2010)

    Google Scholar 

  11. M Benghanem, K O Daffallah and A Almohammedi Results Phys. 8 949 (2018)

    ADS  Google Scholar 

  12. B Liu and R Jordan ASHRAE Trans. 3 526 (1961)

    Google Scholar 

  13. A M Noorian, I Moradi and G A Kamali Renew. Energy 33 1406 (2008)

    Google Scholar 

  14. M Benghanem Appl. Energy 88 1427 (2011)

    Google Scholar 

  15. B Jamil and A T Siddiqui J. Atmos. Solar Terr. Phys. 157 16 (2017)

    ADS  Google Scholar 

  16. O K Tarek, A M R Makbul and A A T Yusuf Renew. Sustain. Energy Rev. 65 626 (2016)

    Google Scholar 

  17. H Darhmaoui and D Lahjouji Energy Procedia 42 426 (2013)

    Google Scholar 

  18. B Jamil, A T Siddiqui and D C Denkenberger Environ. Prog. Sustain. Energy 38 1 (2019)

    Google Scholar 

  19. W G Le Roux Renew. Energy 96 603 (2016)

    Google Scholar 

  20. K Bakirci J. Atmos. Solar Terr. Phys. 152 41 (2017)

    ADS  Google Scholar 

  21. N Bailek, K Bouchouicha, N Aoun, M El-Shimy, B Jamil and A Mostafaeipour Sustain. Energy Technol. Assess. 28 96 (2018)

    Google Scholar 

  22. M J Ahmad and G N Tiwari Open Renew. Energy J. 2 19 (2009)

    ADS  Google Scholar 

  23. B Jamil, A T Siddiqui and N. Akhtar Eng. Sci. Technol. Int. J. 19 1826 (2016)

    Google Scholar 

  24. C K Pandey and A K Katiyar Appl. Energy 88 1455 (2011)

    Google Scholar 

  25. A Ben Othman, K Belkilani, M Besbes Energy Rep. 4 101 (2018)

    Google Scholar 

  26. L Fenga, A Lin, L Wang, W Qin, W Gong Renew. Sustain. Energy Rev. 94 168 (2018)

    Google Scholar 

  27. H Aras, O Balli and A Hepbasli Energy Convers. Manag. 47 2240 (2006)

    Google Scholar 

  28. K Bakirci Renew. Sustain. Energy Rev. 16 6149 (2012)

    Google Scholar 

  29. S Tarhan and A Sarı Energy Convers Manag. 46 605 (2005)

    Google Scholar 

  30. M Iqbal Sol. Energy 23 169 (1979)

    ADS  Google Scholar 

  31. Y Jiang Appl. Energy 86 1458 (2009)

    Google Scholar 

  32. D Erbs, S Klein and J Duffie Sol. Energy 28 293 (1982)

    ADS  Google Scholar 

  33. K Ulgen and A Hepbasli Energy Convers. Manag. 50 149 (2009)

    Google Scholar 

  34. C K Pandey and A Katiyar Energy 34 1792 (2009)

    Google Scholar 

  35. S Barbaro, G Cannata, S Coppolino, C Leone and E Sinagra Sol. Energy 26 429 (1981)

    ADS  Google Scholar 

  36. B Y Liu and R C Jordan Sol. Energy 4 1 (1960)

    ADS  Google Scholar 

  37. Y Jiang J. Energy Eng. 135 107 (2009)

    Google Scholar 

  38. G Lewis Sol. Energy 31 125 (1983)

    ADS  Google Scholar 

  39. J R Howell, R B Bannerot and G C Vliet Solar-Thermal Energy Systems Analysis and Design (New York: McGraw-Hill, Inc.) (1982)

    Google Scholar 

  40. J A Duffie and W A Beckman Solar Engineering of Thermal Processes (New York: Wiley) (1991)

    Google Scholar 

  41. E D Mehleri, P L Zervas, H Sarimveis, J A Palyvos and N C Markatos Renew. Energy 11 2468 (2010)

    Google Scholar 

  42. J A Duffie and B WA Solar engineering of thermal processes, 3rd edn. (New York: Wiley) (2006)

    Google Scholar 

  43. F Samadi, K A Woodbury and J V Beck Int. J. Heat Mass Transf. 122 1116 (2018)

    Google Scholar 

  44. R H Hardin and N J A Sloane J. Stat. Plan. Inference 37 339 (1993)

    Google Scholar 

  45. C V Tao and Y Hu Photogramm. Eng. Remote Sens. 67 1347 (2001)

    Google Scholar 

  46. NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/index.htm

  47. C C Y Ma and M Iqbal Solar Energy 31 313 (1983)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electric-Electronic Engineering, Faculty of Engineering and Natural Sciences, Tokat Gaziosmanpaşa University, 60150, Tokat, Turkey

    Cem Emeksiz

Authors
  1. Cem Emeksiz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cem Emeksiz.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Emeksiz, C. The estimation of diffuse solar radiation on tilted surface using created new approaches with rational function modeling. Indian J Phys 94, 1311–1322 (2020). https://doi.org/10.1007/s12648-019-01573-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-019-01573-w

Keywords

PACS Nos.

Search

Navigation