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Modeling of the Global Solar Radiation Series as a Function of Probability Distribution
Current Issue
Volume 6, 2019
Issue 3 (September)
Pages: 35-42   |   Vol. 6, No. 3, September 2019   |   Follow on         
Paper in PDF Downloads: 56   Since Nov. 13, 2019 Views: 1132   Since Nov. 13, 2019
Authors
[1]
Amaury de Souza, Physics Institute, Federal University of Mato Grosso do Sul, Mato Grosso do Sul, Brazil.
[2]
Razika Ihaddadene, Department of Mechanical Engineering, Med Boudiaf University, M'Sila, Algeria.
[3]
Nabila Haddadene, Department of Mechanical Engineering, Med Boudiaf University, M'Sila, Algeria.
[4]
Pelumi Oguntunde, Department of Mathematics, Covenant University, Ota, Nigeria.
[5]
Hamilton Pavao Hamilton Pavao, Physics Institute, Federal University of Mato Grosso do Sul, Mato Grosso do Sul, Brazil.
[6]
Widinei Fernandes, Physics Institute, Federal University of Mato Grosso do Sul, Mato Grosso do Sul, Brazil.
[7]
José Francisco de Oliveira Júnior, Institute of Atmospheric Sciences, Universidade Federal de Alagoas, Maceió, Brazil.
[8]
Daniel Gomes Soares, Instituto Federal Catarinense, Rio do Sul, Santa Catarina, Brazil.
[9]
Ivana Pobocikova, Department of Applied Mathematics, University of Žilina Univerzitná 1, Žilina, Slovakia.
[10]
Marcel Carvalho Abreu, Department of Environments Science, Universidade Federal Rural do Rio de Janeiro, Rio de Janeiro, Brazil.
[11]
Cícero Manoel dos Santos, Faculty of Agronomic Engineering, Federal University of Para, Altamira, PA, Brasil.
Abstract
The use of probability density functions (pdf) is directly linked to the nature of the data to which they relate. Some have good estimation capacity for small number of data, others require a large number of observations. In this study, the most probability distribution function for modeling the global solar radiation in Campo Grande, MS (Brazil) was determined. The global solar radiation data used for the analysis consists of daily average global solar radiation collected from University of Mato Grosso do Sul which span over the period of one year from January 2016 to December 2016. Various distribution functions were tested in this study and the most suitable one is determined using four different goodness of fit tests. The tested distributions used are Weibull, Rayleigh, Gamma, Lognormal, Rician and Frechet distributions. Four performance indicators; Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and Coefficient of Determination (R 2) were calculated to evaluate the adequacy criteria of the chosen distributions. The best distribution that fits well the global solar radiation observations in Compo Grande region was the Frechet distribution, followed by Weibull and Rician distributions. The worst distributions are given by Rayleigh and Lognormal. This paper is useful as first-hand information in the prediction of future global solar radiation for Campo Grande having known the past behavior and for fixing the missing data.
Keywords
Probabilistic Distribution Function, Cumulative Distribution Function, Global Solar Radiation, Campo Grande
Reference
[1]
Catalunha, M. J., Sediyama, G. C., Leal, B. G., Soares, C. P. B., Ribeiro, A. Aplicação De Cinco Funções Densidade De Probabilidade A Séries De Precipitação Pluvial No Estado De Minas Gerais, Revista Brasileira De Agrometeorologia, (2002), 10 (1), 153-162.
[2]
Souza, A. Ihaddadene, R. Ihaddadene, N. and Oguntunde, P. E. Clarity Index Analysis and Modeling Using Probability Distribution Functions in Campo Grande-MS, Brazil. J. Sol. Energy Eng. (May 08, 2019) 141 (6), doi: 10.1115/1.4043615.
[3]
Ayodele, T. R. Determination Of Probability Distribution Function For Modelling Global Solar Radiation: Case Study Of Ibadan, Nigeria, International Journal Of Applied Science And Engineering, (2015), 13 (3), 233-245.
[4]
Kudish, A. I., Ianetz, A. 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, (1996), 37 (4), 405-416.
[5]
Bendt, P., Collares-Pereira, M., Rabl, A. The Frequency Distribution of Daily Insolation Values, Solar Energy, (1981), 27, 1-5.
[6]
Saunier, G. Y., Reddy, T. A., Kumar, S. A Monthly Probability Distribution Function Of Daily Global Irradiation Values Appropriate For Both Tropical And Temperate Locations, Solar Energy, (1987), 38, 169-177.
[7]
Akuffo, F. O., Brew-Hammond, A. The Frequency Distribution Of Daily Global Irradiation At Kumasi, Solar Energy, (1993), 50, 145-154. 8. Hollands, K. G. T., Huget, R. G. A Probability Density Function for The Clearness Index With Applications, Solar Energy, (1983), 30, 235-253.
[8]
Tovar, J., Olmo, F. J., Alados-Arboledas, L.. One-Minute Global Irradiance Probability Density Distributions Conditioned To The Optical Air Mass, Solar Energy, (1998), 62, 387-393.
[9]
Babu, K. S., Satyamurty, V. V. Frequency Distribution Of Daily Clearness Indices Through Generalized Parameters, Solar Energy, (2001), 70, 35-43.
[10]
Assuncao, H. F., Escobedo, J. F., Oliveira, A. P.. 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, (2007), 90, 235-248.
[11]
DeAssis, J. P, Batista, B. D. O., Sobrinho, J. E., Santos, W. O. Ajuste De Seis Distribuições Densidade De Probabilidade À Séries Históricas De Radiação Solar, EmMossoró/Rn. Revista Verde (Mossoró–Rn–Brasil). (2010.) V. 5, N. 4, P. 228–237.
[12]
Ettoumi, F. Y., Mefti, A., Adane, A., Bouroubi, M. Y. Statistical Analysis Of Solar Measurements In Algeria Using Beta Distribution, Renewable Energy, (2002), 26, 47-67.
[13]
Jurado, M., Caridad, J. M., Ruiz, V.. Statistical Distribution Of The Clearness Index With Radiation Data Integrated Over Five Minute Intervals, Solar Energy, (1995), 55, 469-473.
[14]
Soubdhan, T., Emilion, R., Calif, R. Classification Of Daily Solar Radiation Distributions Using A Mixture Of Dirichlet Distributions, Solar Energy, (2009), 83, 1056-1063.
[15]
Amaury de Souza, [a]* Soetânia S. de Oliveira, [b] Flavio Aristone, [a] Zaccheus Olaofe, [c] Shiva Prashanth Kumar Kodicherla, [d] Milica Arsić, [e] Nabila Ihaddadene [f] and Ihaddadene Razika [g] MODELING OF THE FUNCTION OF THE OZONE CONCENTRATION DISTRIBUTION OF SURFACE TO URBAN AREAS. Eur. Chem. Bull. 2018, 7 (3), 98-105 DOI: 10.17628/ecb.2018.7.98-105.
[16]
Olaofe, Z. O., Folly, K. A. Statistical Analysis Of Wind Resources At Darling For Energy Production, International Journal Of Renewable Energy Research, (2012), 2 (2), 250-251.
[17]
Oguntunde, P. E., Odetunmibi, O. A., Adejumo, A. O. A Study Of Probability Models In Monitoring Environmental Pollution In Nigeria, Journal of Probabilty And Statistics, (2014), ArticleId864965, 6 Pages.
[18]
Noor, N. M., Tan, C. Y., Ramli, N. A., Yahaya, A. S., Yusof, N. F. F. M. Assessment of Various Probability Distributions To Model Pm10 Concentration For Industrialized Area In Peninsula Malaysia: A Case Study In Shah Alam And Nilai. Aust. J. BasicAppl. Sci., (2011), 5 (12), 2796-2811.
[19]
Olaofe Z. O., Assessment of the offshore wind speed distributions at selected stations in the South-West Coast, Nigeria; Int. J. Renew. Energy Res., 2017, 7 (2), 565-577.
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