Skip to main content
SpringerLink
Log in

Experimental Verification of Models for Conversion of Total Solar Radiation from a Horizontal to Inclined Plane under Climatic Conditions of Moscow

  • SOLAR RADIATION AND FORECASTING
  • Published:
Applied Solar Energy Aims and scope Submit manuscript

Abstract

To solve the main engineering problems in the field of solar energy reliable information is needed on the total solar radiation on an inclined surface. In the overwhelming majority of cases only information on the total solar radiation on a horizontal surface is available. The calculation of radiation on an inclined surface is carried out by sequential application of two joined mathematical models, the so-called horizontal (decomposition) and inclined (diffusion) models. In the study, which is based on measurements in two planes (horizontal and south-oriented, inclined at an angle of 45°), in Moscow conditions, during a 5-year period (from March 1, 2016 to February 28, 2021), the most common 11 horizontal (diurnal) and 15 diffuse models were experimentally verified. A systematic comparison of all possible combinations of models made it possible to generalize the results and draw a conclusion about the errors and applicability for the climatic conditions of the Moscow region for each of the models presented separately and, most importantly, when models are used together. It is shown that a combination of (Tuller and Klucher) models has an acceptable accuracy for engineering tasks in summer, and (Skartveit & Olseth and Tian) in winter.

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.

Similar content being viewed by others

REFERENCES

  1. NASA POWER. Prediction of Worldwide Energy Resources. https://power.larc.nasa.gov/. Accessed June 5, 2021.

  2. World Radiation Data Center. http://wrdc.mgo.rssi.ru/wwwrootnew/wrdc_ru_new.htm. Accessed June 5, 2021.

  3. Solar radiation and PV power forecast. Solargis. https://solargis.com/products/forecast/overview. Accessed September 14, 2020.

  4. DWD. Our Services. Open Data. Open Data Server. https://opendata.dwd.de/weather/nwp/. Accessed June 5. 2021.

  5. Daus, Yu.V., Pavlov, K.A., Yudaev, I.V., and Dyachenko, V.V., Increasing solar radiation flux on the surface of flat-plate solar power plants in Kamchatka krai conditions, Appl. Sol. Energy, 2019, vol. 55, no. 2, pp. 101–105.

    Article  Google Scholar 

  6. Hua, Y., He, W., and Liu, P., Optimum tilt angles of solar panels: a case study for Gansu province, northwest China, Appl. Sol. Energy, 2020, vol. 56, no. 5, pp. 388–396.

    Article  Google Scholar 

  7. Komilov, A.G., Algorithm for multivariate solution of mathematical models in MATLAB to create a database of environmental parameters. Appl. Sol. Energy, 2020, vol. 56, no. 1, pp. 63–69.

    Article  Google Scholar 

  8. Daus, Yu.V., Kharchenko, V.V., and Yudaev, I.V., Managing spatial orientation of photovoltaic module to obtain the maximum of electric power generation at preset point of time, Appl. Sol. Energy, 2018, vol. 54, no. 6, pp. 400–405.

    Article  Google Scholar 

  9. Frid, S.E., Simonov, V.M., Lisitskaya, N.V., Avezova, N.R., and Khaitmukhamedov, A.E., Efficiency of solar trackers and bifacial photovoltaic panels for southern regions of the Russian Federation and the Republic of Uzbekistan, Appl. Sol. Energy, 2020, vol. 56, no. 6, pp. 425–430.

    Article  Google Scholar 

  10. Duffie, J. and Beckman, W., Solar Engineering of Thermal Processes, New York: Wiley, 2013.

    Book  Google Scholar 

  11. Tuller, S.E., The relationship between diffuse, total and extraterrestrial solar radiation, Sol. Energy, 1976, vol. 18, p. 259.

    Article  Google Scholar 

  12. Liu, B.Y.H. and Jordan, R.C., The interrelationships and characteristic distribution of direct, diffuse and total solar radiation, Sol. Energy, 1960, vol. 4. pp. 1–19.

    Article  Google Scholar 

  13. De Jong, J.B.R.M., Een karakterisering van de zonnestraling in Nederland, Doctor-aalverslag, Vakgroep Fysiche Aspecten van de Gebouwde Omgeving afd. Bouwkunde en Vakgroep Warmte-en Stromingstechnieken afd. Werktuigbouwkunde, Technische Hogeschool (Techn. Univ.), Eindhoven, Netherlands, 1980.

    Google Scholar 

  14. Collares-Pereira, M. and Rabl, A., The average distribution of solar radiation-correlations between diffuse and hemispherical and between daily and hourly insolation values, Sol. Energy, 1979, vol. 22, pp. 155–164.

    Article  Google Scholar 

  15. Rao, C.N., Bradley, W.A., and Lee, T.Y., The diffuse component of the daily global solar irradiation at Corvallis, Oregon (USA), Sol. Energy, 1984, vol. 32. pp. 637–641.

    Article  Google Scholar 

  16. Muneer, T. and Hawas, M., Correlation between daily diffuse and global radiation for India, Energy Convers. Manage., 1984, vol. 24, pp. 151–154.

    Article  Google Scholar 

  17. Saluja, G.S. and Muneer, T., Correlation between daily diffuse and global irradiation for the UK, Build. Serv. Eng. Res. Technol., 1985, vol. 6, pp. 103–105.

    Article  Google Scholar 

  18. Newland, F.J., A study of solar radiation models for the coastal region of south China, Sol. Energy, 1989, vol. 43, pp. 227–235.

    Article  Google Scholar 

  19. Erbs, D.G., Klein, S.A., and Duffle, J.A., Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation, Sol. Energy, 1982, vol. 28, pp. 293–302.

    Article  Google Scholar 

  20. Lam, J.C. and Li, D.H.W., Correlation between global solar radiation and its direct and diffuse components, Build. Environ., 1996, vol. 31, pp. 527–535.

    Article  Google Scholar 

  21. Skartveit, A. and Olseth, J.A., A model for the diffuse fraction of hourly global radiation, Sol. Energy, 1987, vol. 38, no. 4, pp. 271–274.

    Article  Google Scholar 

  22. Liu, B. and Jordan, R., Daily insolation on surfaces tilted towards equator, ASHRAE, 1961, pp. 53–59.

    Google Scholar 

  23. Badescu, V., 3D isotropic approximation for solar diffuse irradiance on tilted surfaces, Renewable Energy, 2002, vol. 26, pp. 221–233.

    Article  Google Scholar 

  24. Koronakis, P.S., On the choice of the angle of tilt for south facing solar collectors in the Athens basin area, Sol. Energy, 1986, vol. 36, pp. 217–225.

    Article  Google Scholar 

  25. Tian, Y.Q., Davies-Colley, R.J., Gong, P., and Thorrold, B.W., Estimating solar radiation on slopes of arbitrary aspect, Agric. For. Meteorol., 2001, vol. 109, pp. 67–74.

    Article  Google Scholar 

  26. Temps, R.C. and Coulson, K.L., Solar radiation incident upon slopes of different orientations, Sol. Energy, 1977, vol. 19, pp. 179–184.

    Article  Google Scholar 

  27. Klucher, T.M., Evaluation of models to predict insolation on tilted surfaces, Sol. Energy, 1979, vol. 23, pp. 111–114.

    Article  Google Scholar 

  28. Hay, J. and Davies, J., Calculation of monthly mean solar radiation for horizontal and inclined surfaces, Sol. Energy, 1980, vol. 23, pp. 301–307.

    Article  Google Scholar 

  29. Reindl, D.T., Evaluation of hourly tilted surface radiation models, Sol. Energy, 1990, vol. 45, p. 90.

    Article  Google Scholar 

  30. Bugler, J.W., The determination of hourly insolation on an inclined plane using a diffuse irradiance model based on hourly measured global horizontal insolation, Sol. Energy, 1977, vol. 19, p. 477.

    Article  Google Scholar 

  31. Ma, C. and Iqbal, M., Statistical comparison of models for estimating solar radiation on inclined surfaces, Sol. Energy, 1983, vol. 31, pp. 313−317.

    Article  Google Scholar 

  32. Muneer, T., Solar Radiation and Daylight Models, Oxford: Elsevier Butterworth-Heinemann, 2004, 2nd ed.

    Google Scholar 

  33. Gueymard, C., An anisotropic solar irradiance model for tilted surfaces and its comparison with selected engineering algorithms, Sol. Energy, 1987, vol. 38, no. 5, pp. 367–386.

    Article  Google Scholar 

  34. Skartveit, A. and Olseth, J., Modelling slope irradiance at high latitudes, Sol. Energy, 1986, vol. 36, p. 333.

    Article  Google Scholar 

  35. Perez, R., Seals, R., Ineichen, P., Stewart, R., and Menicucci, D., A new simplified version of the perez diffuse irradiance model for tilted surfaces, Sol. Energy, 1987, vol. 39, p. 221.

    Article  Google Scholar 

  36. Willmott, C.J., On the climatic optimization of the tilt and azimuth of flat-plate solar collectors, Sol. Energy, 1982, vol. 28, pp. 205–216.

    Article  Google Scholar 

  37. Stadnik, V.V., Gorbarenko, E.V., Shilovtseva, O.A., and Zadvornykh, V.A., Comparison of the calculated and measured values of the total and scattered radiation entering the inclined surfaces, according to observations at the meteorological observatory of Moscow State University, Tr. Glav. Geofiz. Observ., 2016, vol. 581, pp. 138–154.

    Google Scholar 

  38. Ma, C.C.Y. and Iqbal, M., Statistical comparison of models for estimating solar radiation on inclined surfaces, Sol. Energy, 1983, vol. 31, no. 3, pp. 313–317.

    Article  Google Scholar 

  39. Kudish, A.I. and Ianetz, A., Evaluation of the relative ability of three models, the isotropic, Klucher and Hay, to predict the global radiation on a tilted surface in Beer Sheva, Israel, Energy Convers. Manage., 1991, vol. 32, pp. 387–394.

    Article  Google Scholar 

  40. Evseev, E. and Kudish, A., The assessment of different models to predict the global solar radiation on a surface tilted to the south, Sol. Energy, 2009, vol. 83, pp. 377–388.

    Article  Google Scholar 

  41. Horváth, M. and Csoknyai, T., Evaluation of solar energy calculation methods for 45° inclined, south facing surface, Energy Procedia, 2015, vol. 78, pp. 465–470.

    Article  Google Scholar 

  42. Włodarczyk, D. and Nowak, H., Statistical analysis of solar radiation models onto inclined planes for climatic conditions of Lower Silesia in Poland, Arch. Civ. Mech. Eng., 2009, vol. 9, pp. 127–144.

    Article  Google Scholar 

  43. Noorian, A.M., Moradi, I., and Kamali, G.A., Evaluation of 12 models to estimate hourly diffuse irradiation on inclined surfaces, Renewable Energy, 2008, vol. 33, pp. 1406–1412.

    Article  Google Scholar 

  44. Loutzenhiser, P.G., Manz, H., Felsmann, C., Strachan, P.A., Frank, T., and Maxwell, G.M., Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation, Sol. Energy, 2007, vol. 81, pp. 254–267.

    Article  Google Scholar 

  45. Demain, C., Journée, M., and Bertrand, C., Evaluation of different models to estimate the global solar radiation on inclined surfaces, Renewable Energy, 2013, vol. 50, pp. 710–721.

    Article  Google Scholar 

  46. Bindi, M., Miglietta, F., and Zipoli, G., Different methods for separating diffuse and direct components of solar radiation and their application in crop growth models, Climate Res., 1992, vol. 2, pp. 47–54.

    Article  Google Scholar 

  47. De Miguel, A., Bilbao, J., Aguiar, R., Kambezidis, H., and Negro, E., Diffuse solar irradiation model evaluation in the North Mediterranean belt area, Sol. Energy, 2001, vol. 70, no. 2, pp. 143–153.

    Article  Google Scholar 

  48. Padovan, A. and Del Col, D., Measurement and modeling of solar irradiance components on horizontal and tilted planes, Sol. Energy, 2010, vol. 84, pp. 2068–2084.

    Article  Google Scholar 

  49. Notton, G., Cristofari, C., and Muselli, M., Calculation on an hourly basis of solar diffuse irradiations from global data for horizontal surfaces in Ajaccio, Energy Convers. Manage., 2004, vol. 45, p. 2849.

    Article  Google Scholar 

  50. Notton, G., Poggi, P., and Cristofari, C., Predicting hourly solar irradiations on inclined surfaces based on the horizontal measurements: Performances of the association of well-known mathematical models, Energy Convers. Manage., 2006, vol. 47, pp. 1816–1829.

    Article  Google Scholar 

  51. Yang, D., Dong, Z., Nobre, A., Khoo, Y.S., Jirutitijaroen, P., and Walsh, W., Evaluation of transposition and decomposition models for converting global solar irradiance from tilted surface to horizontal in tropical regions, Sol. Energy, 2013, vol. 97, pp. 369–387.

    Article  Google Scholar 

Download references

ACKNOWLEDGMENTS

The work was supported by the Russian Foundation for Basic Research (project no. 19-08-00877).

Author information

Authors and Affiliations

  1. Joint Institute for High Temperatures, Russian Academy of Sciences, 125412, Moscow, Russia

    A. V. Mordynskiy

Authors
  1. A. V. Mordynskiy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Mordynskiy.

Ethics declarations

The author declares that he has no conflict of interest.

Additional information

Translated by A. Muravev

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mordynskiy, A.V. Experimental Verification of Models for Conversion of Total Solar Radiation from a Horizontal to Inclined Plane under Climatic Conditions of Moscow. Appl. Sol. Energy 57, 430–437 (2021). https://doi.org/10.3103/S0003701X21050108

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0003701X21050108

Keywords:

Search

Navigation