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Thermal Science - Online First

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Simplified calculation method of annual incoming solar energy on tilted and oriented surfaces for the Carpathian basin

The present paper aims at introducing a simplified method of manual calculation of annual incoming solar energy on any tilted and oriented surface using annual horizontal global radiation or sunshine duration hours as input. The proposed simplified formula is developed for the Carpathian basin and can be used in 8 countries with a total geographical area of 483 495 km2. In prospect, a similar formula can be determined for other regions applying the presented methodology. In our work we used the following: the open access CarpatClim database as input data, the Liu-Jordan model as detailed method that was validated with measurement data. The simplified method was developed and validated by use of various statistical approaches and methods.
PAPER REVISED: 2018-01-24
PAPER ACCEPTED: 2018-02-08
  1. Lukovic, J., et al., High resolution grid of potential incoming solar radiation for Serbia, Thermal Science, 19 (2015), suppl. 2, pp. 427-435, DOI: 10.2298/TSCI150430134L
  2. Takebayashi, H., et al., Study to examine the potential for solar energy utilization based on the relationship between urban morphology and solar radiation gain on building rooftops and wall surfaces, Solar Energy, 119 (2015), pp. 362-369, DOI: 10.1016/j.solener.2015.05.039
  3. Szabó, G., et al., Preliminary results on the determination of solar energy potential using LiDAR technology, International Review of Applied Sciences and Engineering, 6 (2015), 1, pp. 11-17, DOI: 10.1556/1848.2015.6.1.2
  4. Pavlovi, T. M., et al., Simulation of photovoltaic systems electricity generation using homer software in specific locations in Serbia, Thermal Science, 17 (2013), 2, pp. 333-347, DOI: 10.2298/TSCI120727004P
  5. Angström, A., Solar terrestrial radiation, Quarterly Journal of the Royal Meteorological Society, 50 (1924), 210, pp. 121-126
  6. Prescott, J. A., Evaporation from a water surface in relation to solar radiation, Transactions of the Royal Society of South Australia, 64 (1940), pp. 114-118
  7. Jain, P. C., A model for diffuse and global irradiation on horizontal surfaces, Solar Energy, 45 (1990), 5, pp. 301-308, DOI: 10.1016/0038-092X(90)90015-5
  8. Suehrcke, H., et al., Relationship between sunshine duration and solar radiation, Solar Energy, 92 (2013), pp. 160-171, DOI: 10.1016/j.solener.2013.02.026
  9. Suehrcke, H., On the relationship between duration of sunshine and solar radiation on the earth's surface: Ångström's equation revisited, Solar Energy, 68 (2000), 5, pp. 417-425, DOI: 10.1016/S0038-092X(00)00004-9
  10. Salima, G., Determining Angstrom Constants for Estimating Solar Radiation in Malawi, International Journal of Geosciences, 3 (2012), 2, pp. 391-397, DOI: 10.4236/ijg.2012.32043
  11. Liu, X., et al., Assessing models for parameters of the Ångström-Prescott formula in China, Applied Energy, 96 (2012), pp. 327-338, DOI: 10.1016/j.apenergy.2011.12.083
  12. Bojanowski, J. S., et al., Calibration of solar radiation models for Europe using Meteosat Second Generation and weather station data, Agricultural and Forest Meteorology, 176 (2013), pp. 1-9, DOI: 10.1016/j.agrformet.2013.03.005
  13. Khorasanizadeh, H., Mohammadi, K., Diffuse solar radiation on a horizontal surface: Reviewing and categorizing the empirical models, Renewable and Sustainable Energy Reviews, 53 (2016), pp. 338-362, DOI: 10.1016/j.rser.2015.08.037
  14. Jacovides, C. P., et al., On the diffuse fraction of daily and monthly global radiation for the island of Cyprus, Solar Energy, 56 (1996), 6, pp. 565-572, DOI: 10.1016/0038-092X(96)81162-5
  15. Jin, Z., et al., Estimation of daily diffuse solar radiation in China, Renewable Energy, 29 (2004), 9, pp. 1537-1548, DOI: 10.1016/j.renene.2004.01.014
  16. Liu, B. Y. H., Jordan, R. C., The interrelationship and characteristic distribution of direct, diffuse and total solar radiation, Solar Energy, 4 (1960), 3, pp. 1-19, DOI: 10.1016/0038-092X(60)90062-1
  17. Temps, R. C., Coulson, K. L., Solar radiation incident upon slopes of different orientations, Solar Energy, 19 (1977), 2, pp. 179-184, DOI: 10.1016/0038-092X(77)90056-1
  18. Hay, J. E., Davies, J. A., Calculation of the solar radiation incident on an inclined surface, in Proceedings First Canadian Solar Radiation Data Workshop, 1980, pp. 59-72
  19. Klucher, T. M., Evaluation of models to predict insolation on tilted surfaces, Solar Energy, 23 (1979), 2, pp. 111-114, DOI: 10.1016/0038-092X(79)90110-5
  20. Skartveit, A., Asle Olseth, J., Modelling slope irradiance at high latitudes, Solar Energy, 36 (1986), 4, pp. 333-344, DOI: 10.1016/0038-092X(86)90151-9
  21. Reindl, D. T., et al., Evaluation of hourly tilted surface radiation models, Solar Energy, 45 (1990), 1, pp. 9-17, DOI: 10.1016/0038-092X(90)90061-G
  22. Ma, C. C. Y., Iqbal, M., Statistical comparison of models for estimating solar radiation on inclined surfaces, Solar Energy, 31 (1983), 3, pp. 313-317, DOI: 10.1016/0038-092X(83)90019-1
  23. Kudish, A. I., Ianetz, A., Evaluation of the relative ability of three models, the isotropic, Klutcher and Hay, to predict the global radiation on a tilted surface in Beer Sheva, Israel, Energy Conversion and Management, 32 (1991), 4, pp. 387-394, DOI: 10.1016/0196-8904(91)90057-P
  24. Stone, R. J., Improved statistical procedure for the evaluation of solar radiation estimation models, Solar Energy, 51 (1993), 4, pp. 289-291, DOI: 10.1016/0038-092X(93)90124-7
  25. Diez-Mediavilla, M., et al., Measurement and comparison of diffuse solar irradiance models on inclined surfaces in Valladolid (Spain), Energy Conversion and Management, 46 (2005), 13-14, pp. 2075-2092, DOI: 10.1016/j.enconman.2004.10.023
  26. Evseev, E. G., Kudish, A. I., The assessment of different models to predict the global solar radiation on a surface tilted to the south, Solar Energy, 83 (2009), 3, pp. 377-388, DOI: 10.1016/j.solener.2008.08.010
  27. Gueymard, C. A., Direct and indirect uncertainties in the prediction of tilted irradiance for solar engineering applications, Solar Energy, 83 (2009), 3, pp. 432-444, DOI: 10.1016/j.solener.2008.11.004
  28. Demain, C., et al., Evaluation of different models to estimate the global solar radiation on inclined surfaces, Renewable Energy, 50 (2013), pp. 710-721, DOI: 10.1016/j.renene.2012.07.031
  29. Badescu, V., Assessing the performance of solar radiation computing models and model selection procedures, Journal of Atmospheric and Solar-Terrestrial Physics, 105-106 (2013), pp. 119-134, DOI: 10.1016/j.jastp.2013.09.004
  30. ***, CarpatClim, 2015,
  31. Martin Bland, J., Altman, D. G., Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement, The Lancet, 327 (1986), 8476, pp. 307-310, DOI: 10.1016/S0140-6736(86)90837-8
  32. Horváth, M., Csoknyai, T., Evaluation of Solar Energy Calculation Methods for 45° Inclined, South Facing Surface, Energy Procedia, 78 (2015), pp. 465-470, DOI: 10.1016/j.egypro.2015.11.700
  33. Devore, J. L., Probability and Statistics for Engineering and the Sciences, 8. kiadás. Brooks/Cole, Boston, 2011