International Journal of Applied Science and Engineering
Published by Chaoyang University of Technology

Tian Pau Chang1

Department of Computer Science and Information Engineering, Nankai University of Technology, Nantou, Taiwan, R.O.C.

Download Citation: |
Download PDF


ABSTRACT

The amount of daily irradiation received for a particular area is one of the most important meteorological parameters for many application fields. In this paper, the frequency distributions of global radiations are investigated using four kinds of probability density functions, i.e. the Weibull function, logistic function, normal function and lognormal function. The radiations observed at six meteorological stations in Taiwan are selected as sample data to be analyzed. To evaluate the performance of the probability functions both the Kolmogorov-Smirnov test and the root mean square errors are considered as judgment criteria. The results show that all the four probability functions are applicable for stations where weather conditions are relatively steady throughout the year as in Taichung and Tainan. While for stations revealing more dispersive distribution as in Hualien and Taitung, the lognormal function describes the frequency distribution quite better than other three functions. On the whole the lognormal function performs best followed by the normal function; the Weibull function widely used in other fields seems to be not appropriate in this case.


Keywords: global radiation; frequency distribution; probability density function; Kolmogorov-Smirnov test; root mean square error.


Share this article with your colleagues

 


REFERENCES

  1. [1] Chang, T. P. 2009. Performance evaluation for solar collectors in Taiwan. Energy, 34: 32-40.

  2. [2] Shu, N., Kameda, N., Kishida, Y., and Sonoda, H. 2006. Experimental and theoretical study on the optimal tilt angle of photovoltaic panels. Journal of Asian Architecture and Building Engineering, 5: 399-405.

  3. [3] Gueymard, C. A. 2003. Direct solar transmittance and irradiance predictions with broadband models. Part I: detailed theoretical performance assessment. Solar Energy, 74, 5: 355-379.

  4. [4] Gueymard, C. A. 2003. Direct solar transmittance and irradiance predictions with broadband models. Part II: validation with high-quality measurements. Solar Energy, 74, 5: 381-395.

  5. [5] Kudish, A. I. and Ianetz, A. 1996. Analysis of daily clearness index, global and beam radiation for Beer Sheva, Israel: Partition according to day type and statistical analysis. Energy Conversion and Management, 37, 4: 405-416.

  6. [6] Bendt, P., Collares-Pereira, M., and Rabl, A. 1981. The frequency distribution of daily insolation values. Solar Energy, 27: 1-5.

  7. [7] Saunier, G. Y., Reddy, T. A., and Kumar, S. 1987. A monthly probability distribution function of daily global irradiation values appropriate for both tropical and temperate locations. Solar Energy, 38: 169-177.

  8. [8] Akuffo, F. O. and Brew-Hammond, A. 1993. The frequency distribution of daily global irradiation at Kumasi. Solar Energy, 50: 145-154.

  9. [9] Tovar, J., Pozo-Vazquez, D., Batlles, J., Lopez, G., and Munoz-Vicente, D. 2004. Proposal of a function for modeling the hourly frequency distributions of photosynthetically active radiation. Theoreti-cal and Applied Climatology, 79: 71-79.

  10. [10] Hollands, K. G. T., and Huget, R. G. 1983. A probability density function for the clearness index with applications. Solar Energy, 30: 235-253.

  11. [11] Tovar, J., Olmo, F. J., and Alados- Arboledas, L. 1998. One-minute global irradiance probability density distributions conditioned to the optical air mass. Solar Energy, 62: 387-393.

  12. [12] Babu, K. S. and Satyamurty, V. V. 2001. Frequency distribution of daily clearness indices through generalized parameters. Solar Energy, 70: 35-43.

  13. [13] Assuncao, H. F., Escobedo, J. F., and Oliveira, A. P. 2007. A new algorithm to estimate sky condition based on 5 minutes-averaged values of clearness index and relative optical air mass. Theoretical and Applied Climatology, 90: 235-248.

  14. [14] Ettoumi, F. Y., Mefti, A., Adane, A., and Bouroubi, M. Y. 2002. Statistical analysis of solar measurements in Algeria using beta distributions. Renewable Energy, 26: 47-67.

  15. [15] Jurado, M., Caridad, J. M., and Ruiz, V. 1995. Statistical distribution of the clearness index with radiation data integrated over five minute intervals. Solar Energy, 55: 469-473.

  16. [16] Soubdhan, T., Emilion, R., and Calif, R. 2009. Classification of daily solar radiation distributions using a mixture of Dirichlet distributions. Solar Energy, 83: 1056-1063.

  17. [17] Liu, C. M. 1996. Climate and weather in Taiwan. Formosa Folkways Publishing Company, Taipei.

  18. [18] Chang, T. P. 2010.Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application. Applied Energy in press, doi: 10.1016/ j.apenergy. 2010.06. 018.

  19. [19] Carta, J. A., Ramirez, P., and Velazquez, S. 2009. A review of wind speed probability distributions used in wind energy analysis Case studies in the Canary Islands. Renewable and Sustainable Energy Reviews, 13: 933-955.

  20. [20] Ucar, A. and Balo, F. 2009. Investigation of wind characteristics and assessment of wind-generation potentiality in Uludag- Bursa, Turkey. Applied Energy, 86: 333-339.

  21. [21] Hogg, R. V., and Craig, A. T. 1988. Introduction to Mathematical Statistics. Fourth edition, Jwang Yuan Publishing Company, Taipei.

  22. [22] Sulaiman, M. Y., Akaak, A. M., Wahab, M. A., Zakaria, A., Sulaiman, Z. A., and Suradi, J. 2002. Wind characteristics of Oman. Energy, 27: 35-46.


ARTICLE INFORMATION



Accepted: 2010-09-23
Available Online: 2010-12-01


Cite this article:

Chang, T.P. 2010. Investigation on frequency distribution of global radiation using different probability density functions. International Journal of Applied Science and Engineering, 8, 99–107. https://doi.org/10.6703/IJASE.2010.8(2).99

Other people also read ...

doaj logo

 

2.3
2022CiteScore
 
 
48th percentile
Powered by  Scopus
 
 

SCImago Journal & Country Rank

IJASE - Most Read Articles

IJASE - Most popular articles