Wind Speed Modelling using Some Modified Gamma
Distribution

Arian Syaputra; Rado Yendra; Muhammad Marizal; Ari Pani Desvina; Rahmadeni

doi:https://doi.org/10.14445/22315373/IJMTT-V68I6P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 6 | Year 2022 | Article Id. IJMTT-V68I6P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I6P509

Wind Speed Modelling using Some Modified Gamma Distribution

Arian Syaputra, Rado Yendra, Muhammad Marizal, Ari Pani Desvina, Rahmadeni

Received	Revised	Accepted	Published
17 Apr 2022	30 May 2022	04 Jun 2022	25 Jun 2022

Citation :

Arian Syaputra, Rado Yendra, Muhammad Marizal, Ari Pani Desvina, Rahmadeni, "Wind Speed Modelling using Some Modified Gamma Distribution," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 6, pp. 87-95, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I6P509

Abstract

Wind speed as a renewable energy source, therefore wind speed data is needed to produce statistical modeling, especially in determining the best probability density function. for this purpose, several modified Gamma distributions will be used and tested to determine the best model to describe wind speed in Pekanbaru. the main goal of this study is to find the best fitting distribution to the daily wind speed measured over Pekanbaru region for the years 1999-2020 by using the four modified Gamma distributions. the maximum likelihood method will be used to get the estimated parameter value from the distribution used in this study. the distributions will be selected based on graphical inspection probability density function (pdf), cumulative distribution function (cdf) and numerical criteria (Akaike’s information criterion (AIC). in most the cases, graphical inspection gave the same result but their AIC result differed. the best fit result was chosen as the distribution with the lowest values of AIC. in general, the Sujatha distribution has been selected as the best model.

Keywords

Mixture distribution, Modified gamma, Renewable energy, Wind speed.

References

[1] J. A. Carta, and P. Ramirez, Analysis of Two-Component Mixture Weibull Statistics for Estimation of Wind Speed Distributions. Renew. Energy, 32 (2007) 518–31.
[2] J. S. Almalki, and J. Yuan, A New Modified Weibull Distribution. Reliability Engineering and System Safety, 111 (2013) 164–170.
[3] J. A. Carta, C. Bueno, P. Ramirez, Statistical Modelling of Directional Wind Speeds using Mixture of Von Mises Distributions: Case Study, Energy Conversion and Management, 49 (2008) 897-907.
[4] R. Kollu, S. R. Rayapudi, S. V. L. Narasimham, and K. M. Pakkurthi, Mixture Probability Distribution Functions to Model Wind Speed Distributions. Int J Energy Environ Eng, 3(27) (2012).
[5] A. I. A. Sayed, and S. R. M. Sabri, Transformed Modified Internal Rate of Return on Gamma Disitribution for Logn Term Stock Investment Modelling. Journal of Management Information and Decision Sciences, 25(S2) (2022) 1-17.
[6] S. Toure, Investigations Into Some Simple Expressions of the Gamma Function in Wind Power Theoretical Estimate by the Weibull Distribution. Journal of Applied Mathematics and Physics, 7(12) (2019) 2990 – 3002. Https://Doi.Org/10.4236/Jamp.2019.712209
[7] M. H. Al Buhairi, A Statistical Analysis of Wind Speed Data and an Assessment of Wind Energy Potential in Taiz-Yemen. Ass. Univ. Bull. Environ. Res. 9(2) (2006) 21-33.
[8] P. Ivana, S. Zuzana, and M. Maria, Application of Four Probability Distributions for Wind Speed Modeling, Precedia Engineering, 192 (2017) 713 – 718.
[9] W. P. L. Fernando, and D. U. J. Sonnadara, Modelling Wind Speed Distributions in Selected Weather Stations. Proceeding of the Technical Session. 23 (2007) 1-6.
[10] S-K. Sim, P. Maass, and P. G. Lind, Wind Speed Modeling by Nested ARIMA Processes. Energies. 12(1) (2019) 69.
[11] P. Chen, T. Pedersen, B. Bak-Jensen, and Z. Chen, ARIMA-Based Time Series Model of Stochastic Wind Power Generation. IEEE Trans. Power Syst. 25(2) (2010) 667–676.
[12] A. Kadhem, N. Wahab, I. Aris, J. Jasni, and A. N. Abdalla, Advanced Wind Speed Prediction Model Based on a Combination of Weibull Distribution and an Artificial Neural Network. Energies. 10(11) (2017) 1744.
[13] D. K. Kaoga, D. Y. Serge, D. Raidandi, and N. Djongyang, Performance Assessment of Two-Parameter Weibull Distribution Methods for Wind Energy Applications in the District of Maroua in Cameroon. Int. J. Sci. Basic Appl. Res. (IJSBAR). 17(1) (2014) 39–59.
[14] M. Al-Muhaini, A. Bizrah, G. Heydt, and M. Kalid, Impact of Wind Speed Modelling on the Predictive Reliability Assessment of Wind-Based Microgrids. the Institution of Engineering and Tecnology. 13(15) (2019) 2947-2956.
[15] E. Dokur, M. Kurban, and S. Cehyan, Wind Speed Modelling Using Inverse Weibull Distrubition: A Case Study for Bilecik, Turkey. International Journal of Energy Applications and Technologies. 3 (2) (2016) 55 – 59.
[16] I. Pobocikova, Z. Sedliackova, and M. Michalkova, Application of Four Probability Distributions for Wind Speed Modeling. Procedia Engineering. 192(2017) 713 – 718.
[17] J. Wang, J. Hu, and K. Ma, Wind Speed Probability Distribution Estimation and Wind Energy Assessment. Elsevier. 60 (2016) 881- 889.
[18] N. Maserran, Integrated Approach for the Determination of an Accurate Wind-Speed Distribution Model. Elsevier. 173(2018) 56-64.
[19] U. Eric, O. Michael, O. Olusola, and C. F. Eze, A Study of Properties and Applications of Gamma Distribution. African Journal of Mathematics and Statistics Studies. 4(2) (2021) 52-65.
[20] A. I. A. Sayed, and S. S. R. Muhammad, A Simulation Study on the Simulated Annealing Algorithm in Estimating the Parameters of Generalized Gamma Distribution. Science and Technology Indonesia. 7(1) (2022). 2580-4405.
[21] C. Tomasi, and Tampiere. Infrared Radiation Extinction Sensitivity to the Modified Gamma Distribution Parameters F or Haze and Fog Droplet Polydispersions. Applied Optics. 15(11) (1976) 2906-2912.
[22] G. W. Petty, and W. Huang, the Modified Gamma Size Distribution Applied to Inhomogeneous and Nonspherical Particles: Key Relationships and Conversions. Journal of the Atmospheric Sciences. 68 (2011) 1460-1473.
[23] M. Mead, M. Nassar, and S. Dey, A Generalization of Generalized Gamma Distributions. Pakistan Journal and Operation Research. 14(1) (2018) 121-138.
[24] A. A. Bakery, W. Zakaria, and O. K. S. K. Mohamed, A New Double Truncated Generalized Gamma Model with Some Applications. Journal of Mathematics. (2021) 1-27.
[25] A. Golubev, Applications and Implications of the Exponentially Modified Gamma Distribution As A Model for Time Variabilities Related to Cell Proliferation and Gene Expression. Journal of Theoretical Biology. 393 (2016) 203-217.
[26] S. Cakmakyapan, and G. Ozel, the Poisson Gamma Distribution for Wind Speed Data. International Conference on Advances in Natural and Applied Sciences. AIP Conf. Proc. (2016) 1726.
[27] R. Shanker, F. Hagos, and S. Sujatha, On Modeling of Lifetimes Data Using One Parameter Akash, Lindley and Exponential Distributions. Biometrics & Biostatistics International Journal, 3(2) (2015) 1-10.
[28] R. Shanker, Shanker Distribution and Its Applications. International Journal of Statistics and Applications, 5(6) (2015) 338-348.
[29] R. Shanker, Sujatha Distribution and Its Applications. Statistics in Transition-New Series. 17(3) (2016) 1-20.