Probability Modeling of Monthly Maximum Sustained Wind Speed in Bangladesh
Wind speed is one the most important parameter of wind energy. However, the probability density functions (pdfs) are usually used to describe the characteristics of wind speed. In literature, several pdfs have been investigated to justify the suitability of modeling the wind speed in different regions all over the world. Therefore, the choice of the pdf is very crucial. This paper, firstly finds the estimates of the parameters of all probability distribution considered in this study to describe wind speed characteristics by using the maximum likelihood method and iterations were carried out with Newton-Raphson technique. Finally, the appropriate pdf for monthly maximum sustained wind speed at Cox’s Bazar in Bangladesh is selected with the help of the Kolmogorov–Smirnov statistic, the coefficient of determination , the Chi-square statistic, Root mean square error (RMSE), AIC and BIC. Here, results depict that, among the distributions considered in this study, the Skewed t (ST) distribution provides the best fit to the wind speed data.
Mandal,A.C.and Islam,M.Q.,Aerodynamics and Design of Wind Turbines, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh, 2001.
Hossain, M. A. and Islam, M. Q., Sailwing Rotor for Pumping Water in Bangladesh, Renewable Energy Review Journal, 4(1),29-35, 1982.
Azad, A. K., Alam, M. M. and Islam, M. R., Statistical Analysis of Wind Gust at Coastal Sites of Bangladesh, International Journal of Energy Machinery, 3(1), 9-17, 2010.
Suresh, R. and Block, D. S., Field Testing of Geared Type Deep Well Wind Pumps in India, Journal of Wind Engineering, 22(2),117-129, 1998.
Blanchard, B. W. and Hsu, S. A., On the Radial Variation of the Tangential Wind Speed outside the Radius of Maximum Wind during Hurricane Wilma, Louisiana: Coastal Studies Institue, Louisiana State University, 2005.
Jan-Hwa Chu, Section 2. Intensity observation and forecast errors, United States Navy, 1999.
Wanninkhof, R., Relationship between wind speed and gas exchange over the ocean, J. Geophys. Res., 97, 7373-7382, 1992.
Justus, C. G., Mani, K. and Mikhail, A. S., Inter-annual and month to-month variations of wind speed, J. Appl. Meteor., 18, 913-920, 1979.
Holland, J. Z., A statistical method for analyzing wave shapes and phase relationships of fluctuating geophysical variables, J. Phys. Oceanogr., 3, 139-155, 1973.
Hennessey, J. O., Some aspects of wind power statistics, J. Appl. Meteor., 16, 119-128, 1977.
Garcia-Bustamante, E., Gonzalex-Rouco, J. F., Jimenez, P. A., Navarro, J. and Montavez, J. P., The influence of the Weibull assumption on monthly wind energy estimation, Wind Energy, 11, 483-502, 2008.
Li, M., and Li, X., MEP-type distribution function: A better alternative to Weibull function for wind speed distributions, Renew. Energy, 30, 1221-1240, 2005.
Lackner, M. A., Rogers, A. L. and Manwell, J. F., Uncertainty analysis in MCP-based wind resource assessment and energy production estimation, J. Sol. Energy Eng., 130, 031006, 2008. doi:10.1115/1.2931499.
Kollu, R., Rayapudi, S. R., Narasimham, S. V. L. and Pakkurthi, K. M. Mixture probability distribution functions to model wind speed distributions, International Journal of Energy and Environmental Engineering, 3, 27, 2012. doi:10.1186/2251-6832-3-27.
Celik, A. N., A statistical analysis of wind power density based on the Weibull and Rayleigh models at the southern region of Turkey, Renew. Energy, 29, 593-604, 2003.
Akdag, S. A, Bagiorgas , H. S. and Mihalakakou, G., Use of two component Weibull mixtures in the analysis of wind speed in the Eastern Mediterranean, Applied Energy, 87(8), 2566-2573, 2010.
Chang, T. P., Estimation of wind energy potential using different probability density functions, Applied Energy, 88(5), 1848-1856, 2011.
Yilmaz, V. and Celik, H. E., A statistical approach to estimate the wind speed distribution: the case of Gelibolu region, Dou niversitesi Dergisi, 9(1), 122-132, 2008.
Safari, B., Modeling wind speed and wind power distributions in Rwanda, Renewable and Sustainable Energy Reviews, 15(2),925-935, 2011.
Hossain, M. M., Abdulla, F. and Majumder, A. K., A Study on Monthly Maximum Wind Speed Probability Distributions at Hazrat Shahajalal and MAG Osmani International Airport of Bangladesh, Jahangirnagar University Journal of Science, 39(2), 11-22, 2016.
Pobo?łkov, I., Sedlia?kov, Z, and Michalkov, M., Application of four probability distributions for wind speed Modeling, Procedia Engineering, 192, 713-718, 2017.
Seguro, J. V. and Lambert, T. W., Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis, Journal of Wind Engineering and Industrial Aerodynamics, 85(1), 75-84, 2000. Doi: 10.1016/S0167-6105(99)00122-1.
Petkovi?, D., Shamshirband, S., Tong, C.W., Al-Shammari, E.T., Generalized adaptive neuro-fuzzy based method for wind speed distribution prediction, Flow Measurement and Instrumentation, 43(1), 47-52, 2015. Doi: 10.1016/j.flowmeasinst.2015.03.003.
Carta, J. A., Ramłrez, P. and Velzquez, S., A review of wind speed probability distributions used in wind energy analysis: Case studies in the Canary Islands, Renewable and Sustainable Energy Reviews, 13(5), 933-955, 2009. Doi: 10.1016/j.rser.2008.05.005.
Ouarda, T. B. M. J., Charron, C., Shin, J. Y., Marpu, P. R., Al Mandoos, A. H., Al-Tamimi, M. H., Ghedira, H., and Al Hosary,T. N., Probability distributions of wind speed in the UAE,Energy Conversion and Management, 93, 414-434, 2015. Doi: 10.1016/j.enconman.2015.01.036.
Ayodele, T. R., Jimoh, A. A., Munda, J. L., and Agee, J. T., Statistical analysis of wind speed and wind power potential of Port Elizabeth using Weibull parameters, Journal of Energy in Southern Africa, 23(2), 30-38, 2012.
Kidmo, D. K., Danwe, R., Doka, S.Y., and Djongyang, N., Statistical analysis of wind speed distribution based on six Weibull Methods for wind power evaluation in Garoua, Cameroon, Revue des Energies Renouvelables, 18(1), 105-125, 2015.
Parajuli, A., A Statistical Analysis of Wind Speed and Power Density Based on Weibull and Rayleigh Models of Jumla, Nepal, Energy and Power Engineering, 8, 271-282, 2016. Doi: 10.4236/epe.2016.87026.
Dokur, E., Kurban, M., Ceyhan, S., Wind speed modelling using inverse weibull distrubition: a case study for Bilecik, Turkey, International Journal of Energy Applications and Technologies, 3(2), 55-59, 2016.
Abdulkarim, A., Abdelkader, S. M., Morrow, D. J., Falade, A. J. and Adediran, Y. A., Statistical analysis of wind speed for electrical power generation in some selected sites in northern Nigeria, Nigerian Journal of Technology, 36(4), 1249-1257, 2017.Doi: 10.4314/njt.v36i4.35.
Weibull, W., A statistical distribution function of wide applicability, J. Appl. Mech. Trans., 18(3), 293-297, 1951.
Johnson, N. L., Kotz, S., Balakrishnan, N., 14: Lognormal Distributions, Continuous Univariate Distributions. Vol. 1., Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics (2nd ed.), New York: John Wiley and Sons, 1994.
Lancaster, H. O., Forerunners of the Pearson Chi-square, Australian Journal of Statistics, 8, 117-126, 1966.
Laplace, P. S., Theorie Analytique des Probabilities, 1836.
Stacy, E. W., A Generalization of the Gamma Distribution, Annals of Mathematical Statistics, 33(3), 1187-1192, 1962.
Ying, A., and Pandey, M. D., The r largest order statistics model for extreme wind speed estimation, J. Wind Eng. and Aerodyn., 95(3), 165-182, 2007.
Cohen, A. C. and Whitten, B. J., Estimation in the Three Parameter Lognormal Distribution, Journal of the American Statistical Association, 75, 399-404, 1980.
Arellano-Valle, R. B. and Azzalini, A., The centered parameterization and related quantities of the skew t distribution, Journal of Multivariate Analysis, 113, 73-90, 2013.
Perks, W. F., On some experiments in the graduation of mortality statistics, Journal of the Institute of Actuaries, 58, 12-57, 1932.
Zeileis, A. and Windberger, T., Fitting and Testing Generalized Logistic Distributions, Package glogis, CRAN, 2014.
Justus, C. G., Hargraves, W. R., and Yalcin, A., Nationwide assessment of potential output from wind-powered generators, J. Appl.Meteorol., 15(7), 673-678, 1976.
Justus, C. G., Hargraves, W. R., Mikhail, A., and Graber, D., Methods for estimating wind speed frequency distributions, J. Appl. Meteorol., 17(3), 350-353, 1978.
Tuller, S. E., and Brett, A. C., The goodness of fit of the Weilbull and Rayleigh distribution to the distributions of observed wind speeds in a topographically diverse area, J. Climatol., 5, 74-94,1985.
Poje, D. and Cividini, B., Assessment of wind energy potential in croatia, Solar Energy, 41(6), 543-554, 1988.
Qin, Z. L., Li, W. Y. and Xiong, X. F., Estimating wind speed probability distribution using kernel density method, Electric Power Syst. Res., 81(12), 2139-2146, 2011.
Usta, I. and Kantar, Y. M., Analysis of some flexible families of distributions for estimation of wind speed distributions, Applied Energy, 89(1), 355-367, 2012.
Cunnane, C., Unbiased plotting positions C a review, J. Hydrol., 37(3-4), 205-222, 1978.
Garcia, A., Torres, J. L., Prieto, E., and De Francisco, A., Fitting wind speed distributions: a case study, Solar Energy, 62(2),139-144, 1998.
Akpinar, E. K., and Akpinar, S., A statistical analysis of wind speed data used in installation of wind energy conversion systems, Energy Convers. Manage., 46(4), 515-532, 2005.
Ramirez, P. and Carta, J. A., The use of wind probability distributions derived from the maximum entropy principle in the analysis of wind energy: A case study, Energy Convers. Manage., 47(15-16), 2564-2577, 2006.
Morgan, E. C., Lackner, M., Vogel, R. M., and Baise, L. G., Probability distributions for offshore wind speeds, Energy Convers. Manage., 52(1), 15-26, 2011.
Soukissian, T., Use of multi-parameter distributions for offshore wind speed modeling: the Johnson SB distribution, Applied Energy, 111, 982-1000, 2013.
Zhang, J., Chowdhury, S., Messac, A., and Castillo, L., A multivariate and multimodal wind distribution model, Renew Energy, 51,436-447, 2013.
Auwera, L., Meyer, F. and Malet, L., The use of the Weibull three parameter model for estimating mean power densities, J. Appl. Meteorol., 19, 819-825, 1980.
Conradsen, K., Nielsen, L. B., and Prahm, L. P., Review of Weibull statistics for estimation of wind speed distributions, J. Climate.Appl. Meteorol., 23(8), 1173-1183, 1984.
Dorvlo, A. S. S., Estimating wind speed distribution, Energy Convers. Manage., 43(17), 2311-2318, 2002.
Nfaoui, H., Buret, J., and Sayigh, A. A. M., Wind characteristics and wind energy potential in Morocco, Solar Energy, 63(1), 51-60, 1998.
Archer, C. L. and Jacobson, M. Z., Spatial and temporal distributions of U.S. winds and wind power at 80 m derived from measurements, J. Geophys Res: Atmosph., 108(D9), 4289, 2003.
Ulgen, K., and Hepbasli, A., Determination of Weibull parameters for wind energy analysis of Izmir, Turkey, Int. J. Energy Res.,26(6), 495-506, 2002.
Kose, R., Ozgur, M. A., Erbas, O. and Tugcu, A., The analysis of wind data and wind energy potential in Kutahya, Turkey, Renew. Sustain. Energy Rev., 8(3), 277-288, 2004.
Jaramillo, O. A., Salda?a, R., and Miranda, U., Wind power potential of Baja California Sur, Mxico, Renew. Energy, 29(13),2087-2100, 2004.
Chellali, F., Khellaf, A., Belouchrani, A., and Khanniche, R. A., comparison between wind speed distributions derived from the maximum entropy principle and Weibull distribution, Case of study; six regions of Algeria, Renew. Sustain. Energy Rev., 16(1),379-385, 2012.
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