MATHEMATICAL MODEL OF SOLAR RADIATION INCIDENT ON AN ARBITRARILY ORIENTED SURFACE FOR ANY REGION IN RUSSIA

The paper deals with an original model of solar radiation incident on an arbitrarily oriented surface. This model has been designed to predict the main characteristics of solar radiation for any geographical point in Russia. The model is based on the isotropic model developed by Liu and Jordan and enables the researches to determine the values of solar radiation incident on an arbitrarily oriented surface at any given time period with the sampling interval of one second. The model implies the use of numerical values of the atmospheric transparency index and the surface albedo obtained from the NASA SSE (Surface meteorology and Solar Energy) database as initial data to ensure precise modeling of the incident solar radiation values including those for regions with no systematic actinometric observations. The paper presents the results of modeling the average daily values of solar radiation for ten Russian settlements located in the region between latitude of 43–62ºN and longitude of 50–158ºE. In order to verify the adequacy of the model, the results of instrumental terrestrial actinometric measurements are taken from meteorological stations included in the World Meteorological Organization network. The verification results show that the average relative model error for the considered meteorological stations does not exceed 11.7% for total solar radiation and 24.5% for scattered radiation. The authors developed the histograms of modeling errors in comparison with data from the World Radiation Data Center and NASA SSE. The analysis of the histograms revealed no systematic errors in the model since the errors were distributed uniformly and symmetrically with respect to the zero level. The paper compares the results of modeling the diurnal variation of solar radiation for 4 typical months of the year in Yekaterinburg with data from the World Radiation Data Center published in the periodic bulletin “Solar Radiation and Radiation Balance Data (The World Network)”. The developed model is implemented as a separate subsystem in MatLab/Simulink to enable its integration into the general model of the energy complex of an arbitrary configuration. The model can be used for studies concerned with the design, development and improvement of the energy systems including solar energy installations.

1. Waldau A.J. PV Status Report 2016. Luxembourg: Publications Office of the European Union, 2016, 84 p. Available in: https://setis.ec.europa.eu/(01.03.2017) (in Eng.)

2. Zhang J. et al. A critical review of the models used to estimate solar radiation. Renewable and Sustainable Energy Reviews, 2017;70:314–329 (in Eng.)

3. Besharatetal F., Dehghan A.A., FaghihA.R. Empirical models for estimating global solar radiation: A review and case study. Renewable and Sustainable Energy Reviews, 2013;21:798–821 (in Eng.)

4. Maleki S.A.M., Hizam H., Gomes C. Estimation of Hourly, Daily and Monthly Global Solar Radiation on Inclined Surfaces: Models Re-Visited // Energies, 2017;10(1). Available in: http://www.mdpi.com/1996-1073/10/1/134/htm/ (01.03.2017) (in Eng.)

5. Katiyar A.K., Pandey C.K. A Review of Solar Radiation Models-Part I. Hindawi Publishing Corporation Journal of Renewable Energy, 2013, Article ID 168048, 11p. Available in: https://www.hindawi.com/journals/jre/2013/168048/ (01.03.2017) (in Eng.)

6. Laue E.G. The measurement of solar spectral irradiance at different terrestrial elevations. Solar Energy, 1970;13(1):43–50 (in Eng.)

7. Robledo L., Soler A. Luminous efficacy of global solar radiation for clear skies. Energy Conversion and Management, 2000;41(16):1769–1779 (in Eng.)

8. Kasten F., Czeplak G. Solar and terrestrial radiation dependent on the amount and type of cloud. Solar Energy, 1980;24(2):177–189 (in Eng.)

9. Gueymard C.A. REST2: High-performance solar radiation model for cloudless-sky irradiance, illuminance, and photosynthetically active radiation – Validation with a benchmark dataset. Solar Energy, 2008;82(3):272–285 (in Eng.)

10. Ineichen P., Perez R. A new air mass independent formulation for the Linke turbidity coefficient. Solar Energy, 2002;73(3):151–157 (in Eng.)

11. Duffie J.A., Beckman W.A. Solar Engineering of Thermal Processes / fourth edition, John Wiley & Sons, Inc., Hoboken, New Jersey, 2013, 910 р. (in Eng.)

12. Piri J., Kisi O. Modelling solar radiation reached to the Earth using ANFIS, NN-ARX, and empirical models (Case studies: Zahedan and Bojnurd stations). Journal of Atmospheric and Solar-Terrestrial Physics, 2015;123:39–47 (in Eng.)

13. Shamshirband S., Mohammadi K., Yee P.L, Petković D., Mostafaeipour A. A comparative evaluation for identifying the suitability of extreme learning machine to predict horizontal global solar radiation. Renewable and Sustainable Energy Reviews, 2015;52:1031–1042 (in Eng.)

14. Adaramola M.S. Estimating global solar radiation using common meteorological data in Akure, Nigeria. Renewable Energy, 2012;47:38–44 (in Eng.)

15. Korachagaon I., Bapat V.N. General formula for the estimation of global solar radiation on earth's surface around the globe. Renewable Energy, 2012;41:394–400 (in Eng.)

16. Erbs D.G., Klein S.A., Duffie J.A. Estimation of the Diffuse Radiation Fraction for Hourly, Daily, and Monthly-Average Global Radiation. Solar Energy, 1982;28(4):293–302 (in Eng.)

17. Orgill J. K., Hollands G.T. Correlation Equation for Hourly Diffuse Radiation on a Horizontal Surface. Solar Energy, 1977;19(4):357–359 (in Eng.)

18. Reindl D.T., Beckman W.A., Duffie J.A. Diffuse Fraction Correlations. Solar Energy, 1990;45(1):1–7 (in Eng.)

19. Liu B.Y.H., Jordan, R.C. Daily insolation on surfaces tilted towards equator. ASHRAE, 1961;10:53–59 (in Eng.)

20. Koronakis, P.S. On the choice of the angle of tilt for south facing solar collectors in the Athens basin area. Solar Energy, 1986;36(3):217–225 (in Eng.)

21. Tian Y.Q., Davies-Colley R.J., Gong P, Thorrold B.W. Estimating solar radiation on slopes of arbitrary aspect // Agricultural and Forest Meteorology. – 2001. – Vol. 109(1). – P. 67–74 (in Eng.)

22. Badescu V. 3D isotropic approximation for solar diffuse irradiance on tilted surfaces. Renewable Energy, 2002;26(2):221–233 (in Eng.)

23. Bugler J.W. 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):477–491 (in Eng.)

24. Klucher T.M. Evaluation of models to predict insolation on tilted surfaces. Solar Energy, 1979;23(2):111–114 (in Eng.)

25. Hay J.E. Calculation of monthly mean solar radiation for horizontal and inclined surfaces. Solar Energy, 1979;23(4):301–307 (in Eng.)

26. Reindl D.T., Beckman W.A., Duffie J.A. Evaluation of hourly tilted surface radiation models. Solar Energy, 1990;45(1):9–17 (in Eng.)

27. The NASA Surface Meteorology and Solar Energy Data Set. Available in: http://eosweb.larc.nasa.gov/sse/ (01.03.2017) (in Eng.)

28. Myers D. R. Solar Radiation: Practical Modeling for Renewable Energy Applications. New York: CRC Press Taylor & Francis Group, 2013, 199 р. (in Eng.)

29. Popel, O.S. Atlas resursov solnechnoi energii na territorii Rossii. Moscow: Izd-vo MFTI Publ., 2010, 86 p. (in Russ.)

30. Stackhouse P.W., Chandler W.S. et all. Surface meteorology and Solar Energy (SSE) Release 6.0 Methodology, Version 3.2.0 June 2, 2016. Available in: https://eosweb.larc.nasa.gov/cgibin/sse/sse.cgi?skip@larc.nasa.gov+s07#s07 (01.03.2017) (in Eng.)

31. World Radiation Data Centre. Available in: http://wrdc.mgo.rssi.ru/ (01.03.2017) (in Eng.)

32. Klein S.A. Calculation of monthly average insolation on tilted surfaces. Solar Energy, 1977;19(4):325–329 (in Eng.)

33. Solnechnaya radiatsiya i radiatsionnyi balans (Mirovaya set'). January 2012 – December 2015. – Sankt-Peterburg: Federal'naya sluzhba Rossii po gidrometeorologii i monitoringu okruzhayushchei sredy, Glavnaya geofizicheskaya observatoriya imeni A.I.Voeikova, Mirovoi tsentr radiatsionnykh dannykh VMO. ISSN 0235 – 4519 (in Russ.)