Solar Radiation Models for the City of Tirana, Albania

Abstract

Mathematical models for evaluating the solar radiation potential are not available for every country or specific sites. In this paper, different solar radiation models (linear, exponential, power) for the city of Tirana-Albania, are built and tested. These models are used to estimate the monthly average total solar radiation on horizontal surface, based on measured data. Measured data include solar radiation on horizontal surface and sunshine duration data, which are used for the development of the models. Calculated and measured values are compared and evaluated by using statistical test methods. Calculated values obtained from the proposed solar radiation models show a good agreement with the measurements. In the best solar radiation model, the percentage error is emax=3.452%, MBE=-0.001465kWh/(m2·day), MPE=-0.015%, RMSE=0.074kWh/(m2·day), and R2=0.998. 

Keywords

• (total solar radiation; horizontal surface; sunshine duration; statistical test values; solar radiation models).

References

1. Albania’s Second National Communication to the Conference of Parties under the United Nations Framework Convention on Climate Change. Tirana, http://unfccc.int/resource/docs/natc/albnc2.pdf Available at: Renewable energies in Albania-Solar energy, Table 1. Accessed http://www.akbn.gov.al/images/pdf/energji-te- rinovueshme/Energjia_Diellore.pdf. Available at: Tirana: Albania, Geographical names. Accessed on April http://www.geographic.org/geographic_names/name.ph p?uni=-168608&fid=283 Available at:
2. J. A. Duffie and W. A. Beckman, Solar engineering of thermal processes, 4-th ed., John Wiley & Sons, New Jersey, 2013.
3. Wetter. Klimadatenbankwetterstation Tirana.Accessed on http://at.wetter.com/reise/laenderinfos/klimadatenbank/? continent=EU&country=EUAL&station=ALXXX0004.
4. S. A. Klein, “Calculation of monthly average insolation on tilted surfaces”, Solar Energy, vol. 19, no. 4, pp. ğ329, 1977.
5. M. P. Thekaekara, “Solar Radiation Measurement: Techniques and Instrumentation”, Solar Energy, vol. 18, no. 4, pp. 309ğ325, 1976. ASTM- American Society
6. Materials.E490-00a.Standard Solar Constant and Zero Air Mass Solar Spectral Irradiance Tables, 2006. and NASA- National Aeronautics and Space
7. Administration. Solar Electromagnetic Radiation.NASA SP-8055, 1971.
8. R. Lazzarin, Sistemisolariattivi, Franco Muzzio& C., Padova, 1981.

9. P. I. Cooper, “The absorption of solar radiation in solar stills”, Solar Energy, vol. 12, no. 3, pp. 333ğ345, A. Ångström, “Solar terrestrial radiation”, Quarterly Journal of the Royal Meteorological Society, vol. 50, no. 210, pp. 121ğ126, 1924.
10. D. V. Hoyt, “Percent of possible sunshine and total cloud cover”, Monthly Weather Review, vol. 105, no. 5, pp 648ğ652, 1977.
11. B. Y. H. Liu and R. C. Jordan, “The interrelationship and characteristic distribution of direct, diffuse and total solar radiation”, Solar Energy, vol. 4, no. 3, pp. 1ğ19, 1960.
12. J. K. Page, “The estimation of monthly mean values of daily total short-wave radiation of vertical and inclined surfaces from sunshine records for latitudes °N–40°S”. in: Proceedings of the UN Conference on New Sources of Energy- Rome 1961, vol. 4-I, pp. ğ390, 1964.
13. J. A. Prescott, “Evaporation from a water surface in relation to solar radiation”. Transactions of the Royal Society of South Australia, vol. 64, pp. 114ğ118, 1940.
14. M. R. Rietveld, “A new method for estimating the regression coefficients in the formula relating solar radiation to sunshine”. Agriculural Meteorology, vol. , no. 2&3, p. 243ğ252, 1978.
15. R. B. Benson, M. V. Paris, J. E. Sherry, and C. G. Justus, “Estimation of daily and monthly direct, diffuse and global solar radiation from sunshine duration measurements”, Solar energy, vol. 32, no. 4, pp. ğ535, 1984.
16. M. Tiris, Ç. Tiris, and I. E. Ture, “Correlations of monthly-average daily global, diffuse and beam radiatons with hours of bright sunshine in Gebze, Turkey”, Energy Conversion and Management, vol. 37, no. 9, pp. 1417ğ1421, 1996.
17. P. C. Jain, “Global irradiation estimation for Italian locations”, Solar and Wind technology, vol. 3, no. 4, pp. 323ğ328, 1986.
18. K. Ulgen and A. Hepbasli, “Solar radiation models.Part 2: Comparison and developing new models”, Energy Sources, vol. 26, no. 5, pp. 521ğ530, M. Paulescu, L. Fara, and E. Tulcan-Paulescu, “Models for obtaining daily global solar irradiation from air temperature data”, Atmospheric Research, vol. , no. 3&4, pp. 227ğ240, 2006.
19. R. G. Allen, “Self-calibrating method for estimating solar radiation from air temperature”, Journal of Hydrologic Engineering, vol. 2, no. 2, pp. 56ğ67, H. O. Menges, C. Ertekin, and M. H. Sonmete, “Evaluation of global solar radiation models for Konya, Turkey”, Energy Conversion Management, vol. 47, no. &19, pp. 3149ğ3173, 2006.
20. Z. Samani, “Estimating solar radiation and evapotranspiration using minimum climatological data”, Journal of Irrigation and Drainage Engineering, vol. , no. 4, pp. 265ğ267, 2000.
21. G. L. Hargreaves, G. H. Hargreaves, and J. P. Riley, “Irrigation water requirements for Senegal River basin”, Journal of Irrigation and Drainage Engineering, vol. 111, no. 3, pp. 265ğ275, 1985.
22. K. L. Bristow and G. S. Campbell, “On the relationship between incoming solar radiation and daily maximum and minimum temperature”, Agriculture and Forest Meteorology, vol. 31, no. 2, pp. 159ğ166, 1984.
23. P. J. Lunde, Solar thermal engineering: Space heating and hot water systems, John Wiley & Sons, New York, 1980.
24. N. A. Elagib and M. G. Mansell, “New approaches for estimating global solar radiation across Sudan”, Energy Conversion and Management, vol. 41, no. 5, pp. ğ434, 2000.
25. J. Almorox and C. Hontoria, “Global solar radiation estimation using sunshine duration in Spain”, Energy Conversion and Management, vol. 45, no. &10, pp. 1529ğ1535, 2004.
26. M. El-Metwally, “Simple new methods to estimate global solar radiation based on meteorological data in Egypt”, Atmospheric Research, vol. 69, no. 3&4, pp. ğ239, 2004.
27. G. Lewis, “Estimates of irradiance over Zimbabwe”, Solar Energy, vol. 31, no. 6, pp. 609ğ612, Gaussian Documentation, 2013. Mathlab R2013b
28. C. W. Richardson, “Weather simulation for crop management models”, Transactions of the American Society of Agricultural Engineers, vol. 28, no. 5, pp. ğ1606, 1985.
29. J. C. Ododo, A. T. Sulaiman, J. Aidan, M. M. Yuguda, and F. A. Ogbu, “The importance of maximum air temperature in the parameterization of solar radiation in Nigeria”, Renewable Energy, vol. 6, no. 7, pp. ğ763, 1995.
30. R. K. Swartman and O. Ogunlade, “Solar radiation estimates from common parameters”, Solar Energy, vol. , no. 3&4, pp. 170ğ172, 1967.
31. Power models. Mathlab R2013b Documentation,
32. Weibull models. Mathlab R2013b Documentation,
33. S. A. Isard, “Evaluation of models for predicting insolation on slopes within the Colorado Alpine Tundra”, Solar Energy, vol. 36, no. 6, pp. 559ğ564, J. A. Davies, M. Abdel-Wahab, and J. E. Howard, “Errors in estimating solar irradiance from a numerical model”, Solar Energy, vol. 32, no. 2, pp. 307ğ309, A. Q. Malik and S. H. Tamam, “Estimation of monthly average daily diffuse radiation for Brunei Darussalam”, Renewable Energy, vol. 6, no. 4, pp. ğ427, 1995.
34. J. A. Davies, M. Abdel-Wahab, and D. C. McKay, “Estimating solar irradiation on horizontal surfaces”, International Journal of Solar Energy, vol. 2, no. 5, pp. ğ424, 1984.
35. A. Zeroual, M. Ankrim, and A. J. Wilkinson, “The diffuse-global correlation: Its application to estimating solar radiation on tilted surfaces in Marrakesh, Morocco”, Renewable Energy, vol. 7, no. 1, pp. 1ğ13, M. Omer, “Diffuse solar radiation over Shambat, Khartoum North”, Renewable Energy, vol. 4, no. 2, pp. ğ233, 1994.
36. H. D. Kambezidis, B. E. Psiloglou, and C. Gueymard, “Measurements and models for total solar irradiance on inclined surface in Athens, Greece”, Solar Energy, vol. 53, no. 2, pp. 177ğ185, 1994.
37. M. Tiris, Ç. Tiris, and İ. E. Türe, “Statistical comparison of models for estimating hourly-diffuse radiation in Gebze, Turkey”, Energy, vol. 21, no. 1, pp. ğ70, 1996.
38. J. A. Martinez-Lozano, M. P. Utrillas, and V. Gomez, “Estimation of the diffuse solar irradiation from global solar irradiation. Daily and monthly average daily values”, Renewable Energy, vol. 4, no. 1, pp. ğ100, 1994.
39. C. Ertekin and O. Yaldiz, “Comparison of some existing models for estimating global solar radiation for Antalya Management, vol. 41, no. 4, pp. 311ğ330, 2000. Energy Conversion and B. Ampratwum and A. S. S. Dorvlo, “Estimation of solar radiation from the number of sunshine hours”,
40. Applied Energy, vol. 63, no. 3, pp. 161ğ167, 1990.
41. M. Hussain, L. Rahman, and M. M. Rahman, “Techniques to obtain predictions of global radiation from sunshine duration”, Renewable Energy, vol. 18, no. 2, pp. 263ğ275, 1999.
42. Sh. Rehman, “Empirical model development and comparison with existing correlations”, Applied Energy, vol. 64, no. 1ğ4, pp. 369ğ378, 1999.
43. T. Toğrul, H. Toğrul, and D. Evin, “Estimation of global solar radiation under clear sky condition in Turkey”, Renewable Energy, vol. 21, no. 2, pp. ğ287, 2000.
44. M. T. Y. Tadros, “Uses of sunshine duration to estimate the global solar radiation over eight meteorological stations in Egypt”, Renewable Energy, vol. 21, no. 2, pp. 231ğ246, 2000.
45. A. A. Sabziparvar and H. Shetaee, “Estimation of global solar radiation in arid and semi-arid climates of East and West Iran”, Energy, vol. 32, no. 5, pp. ğ655,