Using a New Method based on Finsler Geometry for Wind Speed Modelling

Öz

Accurately modelling of wind speed is very important for the assessment of wind energy potential of a certain region. Before the installation of a wind energy conversion system in a region, the wind speed potential of that region needs to be determined and modelled. For this reason, different distribution functions such as two-parameter Weibull, Gamma, Lognormal, Rayleigh etc.  are proposed for accurately modeling wind speed in the literature. In this paper, new probability and cumulative probability density functions based on Finsler geometry are proposed for  wind speed modelling. Two-dimensional Finsler space metric function is obtained for Weibull distribution. Monthly analysis for Yalova,  Turkey is realized  using a new method based on Finsler geometry and two-parameter Weibull distribution. Wind data, consisting of  hourly wind speed records between October 2015-September 2016 were obtained from the Yalova station  of Turkish State Meteorological Service. The performances of the models  are given comparatively by using root mean square error (RMSE).

Anahtar Kelimeler

• Finsler Geometry,Wind Speed,Modelling,Weibull Distribution,Renewable Energy

Kaynakça

1. [1] Saleh H, Aly AA, Abdel-Hady S., "Assessment of different methods used to estimate Weibull distribution parameters for wind speed in Zafarana wind farm, Suez Gulf, Egypt", Energy. 2012 Aug 31;44(1):710-9.
2. [2] S. M. Metev and V. P. Veiko, Laser Assisted Microtechnology, 2nd ed., R. M. Osgood, Jr., Ed. Berlin, Germany: Springer-Verlag, 1998.
3. [3] Garcia A, Torres JL, Prieto E, De Francisco A., "Fitting wind speed distributions: a case study.", Solar energy. 1998 Feb 28;62(2):139-44.
4. [4] Luna RE, Church HW., "Estimation of long-term concentrations using a “universal” wind speed distribution. Journal of Applied Meteorology. 1974 Dec;13(8):910-6.
5. [5] Justus CG, Hargraves WR, Yalcin A., "Nationwide assessment of potential output from wind-powered generators", Journal of applied meteorology. 1976 Jul;15(7):673-8.
6. [6] Kiss P, Jánosi IM., "Comprehensive empirical analysis of ERA-40 surface wind speed distribution over Europe", Energy Conversion and Management. 2008 Aug 31;49(8):2142-51.
7. [7] Bardsley WE. Note on the use of the inverse Gaussian distribution for wind energy applications. Journal of Applied Meteorology. 1980 Sep;19(9):1126-30.
8. [8] Vogel RM, McMahon TA, Chiew FH., "Floodflow frequency model selection in Australia", Journal of Hydrology. 1993 Jun 1;146:421-49.

9. [9] Guttman NB, Hosking JR, Wallis JR., "Regional precipitation quantile values for the continental United States computed from L-moments. Journal of Climate", 1993 Dec;6(12):2326-40.
10. [10] Stedinger JR., "Fitting log normal distributions to hydrologic data", Water Resources Research. 1980 Jun 1;16(3):481-90.
11. [11] Kaminsky FC. "Four probability densities/log-normal, gamma, Weibull, and Rayleigh/and their application to modelling average hourly wind speed", International Solar Energy Society, Annual Meeting 1977 (pp. 19-6).
12. [12] Sherlock RH., "Analyzing winds for frequency and duration" InOn Atmospheric Pollution 1951 (pp. 42-49). American Meteorological Society.
13. [13] Morgan EC, Lackner M, Vogel RM, Baise LG., "Probability distributions for offshore wind speeds", Energy Conversion and Management. 2011 Jan 31;52(1):15-26.
14. [14] Takle ES, Brown JM., "Note on the use of Weibull statistics to characterize wind-speed data", Journal of applied meteorology. 1978 Apr;17(4):556-9.
15. [15] Jaramillo OA, Borja MA., "Wind speed analysis in La Ventosa, Mexico: a bimodal probability distribution case", Renewable Energy. 2004 Aug 31;29(10):1613-30.
16. [16] Rosen K, Van Buskirk R, Garbesi K. "Wind energy potential of coastal Eritrea: an analysis of sparse wind data", Solar energy. 1999 Jun 30;66(3):201-13.
17. [17] Carta JA, Ramirez P, Velazquez S., "A review of wind speed probability distributions used in wind energy analysis: Case studies in the Canary Islands", Renewable and Sustainable Energy Reviews. 2009 Jun 30;13(5):933-55.
18. [18] Shamshirband, S., "Assessing the proficiency of adaptive neuro-fuzzy system to estimate wind power density: Case study of Aligoodarz, Iran." Renewable and Sustainable Energy Reviews 59 (2016): 429-435.
19. [19] Arslan, Oguz. ,"Technoeconomic analysis of electricity generation from wind energy in Kutahya, Turkey.", Energy 35.1 (2010): 120-131.
20. [20] Malik, A., and A. H. Al-Badi. "Economics of wind turbine as an energy fuel saver–a case study for remote application in Oman." Energy 34.10 (2009): 1573-1578.
21. [21] Liu, Feng Jiao, and Tian Pau Chang., "Validity analysis of maximum entropy distribution based on different moment constraints for wind energy assessment." Energy 36.3 (2011): 1820-1826.
22. [22] Chang, Tian-Pau, "Comparative analysis on power curve models of wind turbine generator in estimating capacity factor." Energy 73 (2014): 88-95.
23. [23] Arslan, Talha, Y. Murat Bulut, and Arzu A. Y., "Comparative study of numerical methods for determining Weibull parameters for wind energy potential." Renewable and Sustainable Energy Reviews 40 (2014): 820-825.
24. [24] Mohammadi K, Alavi O, Mostafaeipour A, Goudarzi N, Jalilvand M., "Assessing different parameters estimation methods of Weibull distribution to compute wind power density", Energy Convers and Manage 2016; 108:322-335.
25. [25] Carrasco-Díaz, Magdiel, et al., "An assessment of wind power potential along the coast of Tamaulipas, northeastern Mexico." Renewable Energy 78 (2015): 295-305.
26. [26] Manwell, James F., Jon G. McGowan, and Anthony L. Rogers. Wind energy explained: theory, design and application. John Wiley & Sons, 2010.
27. [27] Mathew, Sathyajith. Wind energy: fundamentals, resource analysis and economics. Vol. 1. Heidelberg: Springer, 2006.
28. [28] Shen, Zhongmin. Lectures on Finsler geometry. Vol. 2001. Singapore: World Scientific, 2001.
29. [29] Z.Shen, Differential geometry of spray and Finsler spaces, Kluwer Academic Publishers, Dordrecht, 2001.
30. [30] Matsumoto, M. "Geodesics of two-dimensional Finsler spaces." Mathematical and computer modelling 20.4 (1994): 1-23.
31. [31] Dokur, Emrah, Ceyhan S., and Kurban M., "Finsler Geometry for Two-Parameter Weibull Distribution Function." Mathematical Problems in Engineering 2017 .