Yusuf ŞAHİN, Melih Burak KOCA, Muhammet Burak KILIÇ

Using genetic algorithms for estimating Weibull parameters with application to wind speed

Renewable energy has become a prominent subject for researchers since fossil fuelreserves have been decreasing and are not promising to meet the energy demandof the future. Wind takes an important place in renewable energy resources andthere is extensive research on wind speed modeling. Herein, one of the mostcommonly used distributions for wind speed modeling is the Weibull distributionwith its simplicity and flexibility. Maximum likelihood (ML) method is the mostfrequently used technique in Weibull parameter estimation. Iterative techniquessuch as Newton-Raphson (NR) use random initial values to obtain the MLestimators of the parameters of the Weibull distribution. Therefore, the success ofthe iterative techniques highly depends on the initial value selection. In order todeliver a solution to the initial value problem, genetic algorithm (GA) isconsidered to obtain the estimators of the model parameters. The ML estimatorsobtained using the GA and NR techniques are compared with the method ofmoments (MoM) estimators via Monte Carlo simulation and wind speedapplications. The results show that the ML estimators obtained using GA presentsuperiority over MoM and the ML estimators obtained using NR.

PDF

___

[1] Hou, Y., Peng, Y., Johnson, A.L. & Shi, J. (2012). Empirical analysis of wind power potential at multiple heights for North Dakota wind observation sites. Energy Science and Technology, 4(1), 1-9. DOI:10.3968/j.est.1923847920120401.289
[2] Sohoni, V., Gupta, S. & Nema, R. (2016). A comparative analysis of wind speed probability distributions for wind power assessment of four sites. Turkish Journal of Electrical Engineering & Computer Sciences, 24(6), 4724-4735. DOI:10.3906/elk-1412-207
[3] Turkan, Y.S., Aydogmus, H.Y. & Erdal, H. (2016). The prediction of the wind speed at different heights by machine learning methods. An International Journal of Optimization and Control: Theories & Applications, 6(2), 179-197. DOI:10.11121/ijocta.01.2016.00315
[4] Koca, M.B., Kılıç, M.B. & Şahin, Y. Assessing wind energy potential using finite mixture distributions. Turkish Journal of Electrical Engineering & Computer Sciences, 27(3), 2276-2294. DOI:10.3906/elk-1802-109
[5] Seguro, J.V., & Lambert, T.W. (2000). Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis. Journal of Wind Engineering and Industrial Aerodynamics, 85, 75-84. DOI:10.1016/S0167-6105(99)00122-1
[6] Akgül, F.G., Şenoğlu, B., & Arslan, T. (2016). An alternative distribution to Weibull for modeling the wind speed data: Inverse Weibull distribution. Energy Conversion and Management, 114, 234-240. DOI:10.1016/j.enconman.2016.02.026
[7] Lun, I.Y.F., & Lam, J.C. (2000). A study of Weibull parameters using long-term wind observations. Renewable Energy, 20, 145-153. DOI:10.1016/s0960-1481(99)00103-2
[8] Arslan, T., Bulut, Y.M., & Yavuz, A.A. (2014). Comparative study of numerical methods for determining Weibull parameters for wind speed modeling. Renewable and Sustainable Energy Reviews, 40, 820-825. DOI:10.1016/j.ser/2014.08.009
[9] Safari, B. (2011). Modeling wind speed and wind power distributions in Rwanda. Renewable and Sustainable Energy Reviews, 15, 925-935. DOI:10.1016/j.ser.2010.11.001
[10] Kaplan, Y.A. (2016). The evaluating of wind energy potential of Osmaniye region with using Weibull and Rayleigh distributions. Süleyman Demirel University Journal of Natural and Applied Sciences, 20(1), 62-71. DOI:10.19113/sdufbed.63806
[11] Kollu, R., Rayapudi, S.R., Narasimham, S.V.L., & Pakkurthi, K.M. (2012). Mixture probability distribution functions to model wind speed distributions. International Journal of Energy and Environmental Engineering, 3(27). DOI:10.1186/2251-6832-3-27
[12] Akpınar, E.K., & Akpınar, S. (2004). Determination of the wind energy potential for Maden-Elazig, Turkey. Energy Conversion and Management, 45, 2901-2914. DOI:10.1016/j.enconman.2003.12.016
[13] Teimouri, M., Hoseini, S.M., & Nadarajah, S. (2013). Comparison of estimation methods for the Weibull distribution. Statistics, 47(1), 93-109. DOI:10.1080/02331888.2011.559657
[14] Akdağ, S.A. & Dinler, A. (2009). A new method to estimate Weibull parameters for wind energy applications. Energy Conversion and Management, 50, 1761-1766. DOI:10.1016/j.enconman.2009.03.020
[15] Saleh, H., Abou El-Azm Aly, A. & Abdel-Hady, S. (2012). Assessment of different methods used to estimate Weibull distribution parameters for wind speed in Zafarana wind farm, Suez Gold, Egypt. Energy, 44, 710-719. DOI:10.1016/j.energy.2012.05.021
[16] Azad. A.K., Rasul, M. G. & Yusaf, T. (2014). Statistical diagnosis of the best Weibull methods for wind power assessment for agricultural applications. Energies, 7, 3056-3085. DOI:10.3390/en7053056
[17] Usta, I., Arik, I., Yenilmez, I. & Kantar, Y.M. (2018). A new estimation approach based on moments for estimating Weibull parameters in wind speed power applications. Energy Conversion and Management, 164, 570-578. DOI:10.1016/j.enconman.2018.03.033
[18] Tu, T.V. & Sano, K. (2013). Genetic algorithm for optimization in adaptive bus signal priority control. An International Journal of Optimization and Control: Theories & Applications, 3(1), 35-43. DOI:10.11121/ijocta.01.2013.00138
[19] Şimşek, B. & Şimşek, E.H. (2017). Assessment and optimization of thermal and fluidity properties of high strength concrete via genetic algorithm. An International Journal of Optimization and Control: Theories & Applications, 7(1), 90-97. DOI:10.11121/ijocta.01.2017.00345
[20] Gençtürk, Y., & Yiğiter, A. (2016). Modelling claim number using a new mixture model: negative binomial gamma distribution. Journal of Statistical Computation and Simulation, 86, 1829-1839. DOI:10.1080/00949655.2015.1085987
[21] Yalçınkaya, A., Şenoğlu, B., & Yolcu, U. (2018). Maximum likelihood estimation for the parameters of skew normal distribution using genetic algorithm. Swarm and Evolutionary Computation, 38, 127-138. DOI:10.1016/j.swevo.2017.07.007
[22] Altunkaynak, B., & Esin, A. (2004). The genetic algorithm method for parameters estimation in nonlinear regression. Gazi University Journal of Science, 17(2), 43-51.
[23] Thomas, G.M., Gerth, R., Velasco, T., & Rabelo, L.C. (1995). Using real-coded genetic algorithms for Weibull parameter estimation. Computers & Industrial Engineering, 29, 377-381. DOI:10.1016/0360-8352(95)00102-7
[24] Henningsen, A., & Toomet, O. (2010). maxLik: A package for maximum likelihood estimation in R. Computational Statistics, 26, 443-458. DOI: 10.1007/s00180-010-0217-1
[25] Scrucca, L. (2013). GA: A package for genetic algorithms in R. Journal of Statistical Software, 53(4), 1-37. DOI: 10.18637/jss.v053.i04
[26] Massey JR, F.J. (1951). The Kolmogorov-Smirnov test for goodness of fıt. Journal of American Statistical Association, 46, 68-78. DOI:10.1080/01621459.1951.10500769