Statistical Diagnosis of the Best Weibull Methods for Wind Power Assessment for Agricultural Applications

The best Weibull distribution methods for the assessment of wind energy potential at different altitudes in desired locations are statistically diagnosed in this study. Seven different methods, namely graphical method (GM), method of moments (MOM), standard deviation method (STDM), maximum likelihood method (MLM), power density method (PDM), modified maximum likelihood method (MMLM) and equivalent energy method (EEM) were used to estimate the Weibull parameters and six statistical tools, namely relative percentage of error, root mean square error (RMSE), mean percentage of error, mean absolute percentage of error, chi-square error and analysis of variance were used to precisely rank the methods. The statistical fittings of the measured and calculated wind speed data are assessed for justifying the performance of the methods. The capacity factor and total energy generated by a small model wind turbine is calculated by numerical integration using Trapezoidal sums and Simpson’s rules. The results show that MOM and MLM are the most efficient methods for determining the value of k and c to fit Weibull distribution curves.

[1]  Olayinka S. Ohunakin,et al.  Assessment of wind energy resources for electricity generation using WECS in North-Central region, Nigeria , 2011 .

[2]  C. Justus,et al.  Height variation of wind speed and wind distributions statistics , 1976 .

[3]  D. Weisser,et al.  A wind energy analysis of Grenada: an estimation using the 'Weibull' density function , 2003 .

[4]  Glen H. Lemon.  Maximum Likelihood Estimation for the Three Parameter Weibull Distribution Based on Censored Samples , 1975 .

[5]  E. Akpinar,et al.  Statistical analysis of wind energy potential on the basis of the Weibull and Rayleigh distributions for Agin-Elazig, Turkey , 2004 .

[6]  Hongxing Yang,et al.  Wind power potential and characteristic analysis of the Pearl River Delta region, China , 2006 .

[7]  Olayinka S. Ohunakin,et al.  Assessment of wind energy potential and the economics of wind power generation in Jos, Plateau State, Nigeria , 2012 .

[8]  Faby Sunny,et al.  Assessment of wind energy potential of Trombay, Mumbai (19.1°N; 72.8°E), India , 1998 .

[9]  Riccardo Burlon,et al.  Stochastic models for wind speed forecasting , 2011 .

[10]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[11]  S. C. Choi,et al.  Maximum Likelihood Estimation of the Parameters of the Gamma Distribution and Their Bias , 1969 .

[12]  W. Rivera,et al.  Wind speed forecasting in the South Coast of Oaxaca, México , 2007 .

[13]  Tian Pau Chang,et al.  Wind energy assessment incorporating particle swarm optimization method , 2011 .

[14]  Ahmed S. Ahmed,et al.  Wind energy as a potential generation source at Ras Benas, Egypt , 2010 .

[15]  Shafiuzzaman K. Khadem,et al.  A pre-feasibility study of wind resources in Kutubdia Island, Bangladesh , 2006 .

[16]  Fawzi A. L. Jowder,et al.  Wind power analysis and site matching of wind turbine generators in Kingdom of Bahrain , 2009 .

[17]  V. Akhmatov.  Influence of Wind Direction on Intense Power Fluctuations in Large Offshore Windfarms in the North Sea , 2007 .

[18]  O. A. Jaramillo,et al.  Wind power potential of Baja California Sur, México , 2004 .

[19]  Seyit Ahmet Akdağ,et al.  A new method to estimate Weibull parameters for wind energy applications , 2009 .

[20]  Frede Blaabjerg,et al.  Wind farm—A power source in future power systems , 2009 .

[21]  R. Hanitsch,et al.  Electricity generation and wind potential assessment at Hurghada, Egypt , 2008 .

[22]  Noor Akma Ibrahim,et al.  Bayesian Analysis of the Survival Function and Failure Rate of Weibull Distribution with Censored Data , 2012 .

[23]  Dost Muhammad Khan,et al.  Statistical Analysis of Wind Speed Data in Pakistan , 2012 .

[24]  Jau-Chuan Ke,et al.  Computation Approaches for Parameter Estimation of Weibull Distribution , 2012 .

[25]  Carla Freitas de Andrade,et al.  Comparison of seven numerical methods for determining Weibull parameters for wind energy generation in the northeast region of Brazil , 2012 .

[26]  T. Chang.  Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application , 2011 .

[27]  Abul Kalam Azad.  Statistical Weibull’s Distribution Analysis for Wind Power of The Two Dimensional Ridge Areas , 2013 .

[28]  S. A. Ahmed,et al.  A Statistical Analysis of Wind Power Density Based on the Weibull and Ralyeigh models of " Penjwen Region " Sulaimani / Iraq , 2012 .

[29]  D. Munz,et al.  Estimation procedure for the Weibull parameters used in the local approach , 1992, International Journal of Fracture.

[30]  Fernando Cruz-Peragón,et al.  Characterization of solar flat plate collectors , 2012 .

[31]  G. S. Watson,et al.  Goodness-of-fit tests on a circle. II , 1961 .

[32]  Jeffrey H. Gove,et al.  Moment and maximum likelihood estimators for Weibull distributions under length- and area-biased sampling , 2003, Environmental and Ecological Statistics.

[33]  P. E. Ugwuoke,et al.  Weibull distribution-based model for prediction of wind potential in Enugu, Nigeria , 2012 .

[34]  Muyiwa S. Adaramola,et al.  Assessment of electricity generation and energy cost of wind energy conversion systems in north-central Nigeria , 2011 .

[35]  Önder Güler,et al.  Evaluation of wind energy investment interest and electricity generation cost analysis for Turkey , 2010 .

[36]  Y. Kantar,et al.  Analysis of wind speed distributions: Wind distribution function derived from minimum cross entropy principles as better alternative to Weibull function , 2008 .

[37]  Fadare D.A.A..  STATISTICAL ANALYSIS OF WIND ENERGY POTENTIAL IN IBADAN, NIGERIA BASED ON WEIBULL DISTRIBUTION FUNCTION , 2008 .

[38]  L. Sedefian,et al.  On the Vertical Extrapolation of Mean Wind Power Density , 1980 .

[39]  Tsang-Jung Chang,et al.  Assessment of wind characteristics and wind turbine characteristics in Taiwan , 2003 .

[40]  A. A. Chen,et al.  Stochastic simulation and forecasting of hourly average wind speed sequences in Jamaica , 1991 .

[41]  Earl P. N. Duque,et al.  Wind resource assessment in the state of Arizona: Inventory, capacity factor, and cost , 2007 .

[42]  Radian Belu,et al.  Wind characteristics and wind energy potential in western Nevada , 2009 .

[43]  E. Akpinar.  A Statistical Investigation of Wind Energy Potential , 2006 .

[44]  Forrest J. Masters,et al.  Peak factor estimation in hurricane surface winds , 2012 .

[45]  A. Celik.  Weibull representative compressed wind speed data for energy and performance calculations of wind energy systems , 2003 .

[46]  A. Dorvlo.  Estimating wind speed distribution , 2002 .

[47]  Qiusheng Li,et al.  Probability distributions of extreme wind speed and its occurrence interval , 2005 .

[48]  Albert H. Moore,et al.  Maximum-Likelihood Estimation of the Parameters of Gamma and Weibull Populations from Complete and from Censored Samples , 1965 .

[49]  B. Rémillard,et al.  Goodness-of-fit tests for copulas: A review and a power study , 2006 .

[50]  Dimitri Kececioglu,et al.  Maximum likelihood estimates, from censored data, for mixed-Weibull distributions , 1992 .

[51]  L. Kamal,et al.  Time series models to simulate and forecast hourly averaged wind speed in Quetta, Pakistan , 1997 .

[52]  M. McCormick,et al.  A fuzzy logic controlled power electronic system for variable speed wind energy conversion systems , 2000 .

[53]  A. Cohen,et al.  Maximum Likelihood Estimation in the Weibull Distribution Based On Complete and On Censored Samples , 1965 .

[54]  A. Sedaghat,et al.  Assessing the wind energy potential locations in province of Semnan in Iran , 2011 .

[55]  Quetzalcoatl Hernandez-Escobedo,et al.  The wind power of Mexico , 2010 .

[56]  K. P. Pandey,et al.  Analysis of wind regimes for energy estimation , 2002 .

[57]  Muyiwa S. Adaramola,et al.  Analysis of wind speed data and wind energy potential in three selected locations in south-east Nigeria , 2012, International Journal of Energy and Environmental Engineering.

[58]  Q. Hernández-Escobedo,et al.  Wind energy resource in Northern Mexico , 2014 .

[59]  Matthew A. Lackner,et al.  Probability distributions for offshore wind speeds , 2009 .

[60]  A. Ilinca,et al.  WIND POTENTIAL ASSESSMENT OF QUEBEC PROVINCE , 2003 .

[61]  Nasrudin Abd Rahim,et al.  Assessment of wind energy potentiality at Kudat and Labuan, Malaysia using Weibull distribution function , 2011 .

[62]  A. Hepbasli,et al.  Determination of Weibull parameters for wind energy analysis of İzmir, Turkey , 2002 .

[63]  J. A. Carta,et al.  The use of wind probability distributions derived from the maximum entropy principle in the analysis of wind energy. A case study , 2006 .

[64]  K. Philippopoulos,et al.  Statistical simulation of wind speed in Athens , Greece based on Weibull and ARMA models , 2010 .

[65]  R. Langlois,et al.  Estimation of Weibull parameters , 1991 .

[66]  R. Zamar,et al.  A multivariate Kolmogorov-Smirnov test of goodness of fit , 1997 .

[67]  E. Erdem,et al.  Comprehensive evaluation of wind speed distribution models: A case study for North Dakota sites , 2010 .

[68]  Omid Nematollahi,et al.  Assessment of wind energy in Iran: A review , 2012 .

[69]  Ali Mostafaeipour,et al.  Using different methods for comprehensive study of wind turbine utilization in Zarrineh, Iran , 2013 .

[70]  A. Keyhani,et al.  An assessment of wind energy potential as a power generation source in the capital of Iran, Tehran , 2010 .

[71]  P. Sorensen,et al.  Power Fluctuations From Large Wind Farms , 2007, IEEE Transactions on Power Systems.

[72]  W. R. Hargraves,et al.  Methods for Estimating Wind Speed Frequency Distributions. , 1978 .

[73]  Quetzalcoatl Hernandez-Escobedo,et al.  Is the wind a periodical phenomenon? The case of Mexico , 2011 .

[74]  B. Safari,et al.  A statistical investigation of wind characteristics and wind energy potential based on the Weibull and Rayleigh models in Rwanda , 2010 .

[75]  Paritosh Bhattacharya,et al.  A Study on Weibull Distribution for Estimating the Parameters , 2009 .

[76]  J. Kyparisis,et al.  A review of maximum likelihood estimation methods for the three-parameter weibull distribution , 1986 .

[77]  T. W. Lambert,et al.  Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis , 2000 .

[78]  A. Celik.  A statistical analysis of wind power density based on the Weibull and Rayleigh models at the southern region of Turkey , 2004 .

[79]  H. Madsen,et al.  Resolving Nonstationary Spectral Information in Wind Speed Time Series Using the Hilbert-Huang Transform , 2010 .

[80]  M. N. Schwartz,et al.  Wind Energy Potential in the United States , 1993 .

[81]  P. S. Dokopoulos,et al.  Wind speed and power forecasting based on spatial correlation models , 1999 .

[82]  Lucy Pao,et al.  Optimal Control of Wind Energy Systems: Towards a Global Approach (Munteanu, I. et al.; 2008) [Bookshelf] , 2009, IEEE Control Systems.

[83]  George Galanis,et al.  Wind power prediction based on numerical and statistical models , 2013 .

[84]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[85]  J. C. Lam,et al.  A study of Weibull parameters using long-term wind observations , 2000 .

[86]  G. C. Montanari,et al.  Comparison of maximum likelihood unbiasing methods for the estimation of the Weibull parameters , 1996 .

[87]  R. Hanitsch,et al.  Evaluation of wind energy potential and electricity generation on the coast of Mediterranean Sea in Egypt , 2006 .

[88]  Ramazan Köse,et al.  The analysis of wind data and wind energy potential in Kutahya, Turkey , 2004 .

[89]  P SardarMaran,et al.  Wind Power Density Estimation using Meteorological Tower Data , 2013 .

[90]  C. Hsieh,et al.  The analysis of offshore islands wind characteristics in Taiwan by Hilbert–Huang transform , 2012 .

[91]  R B D'Agostino,et al.  Maximum likelihood estimation for interval-censored data using a Weibull-based accelerated failure time model. , 1992, Biometrics.

[92]  Arvid Naess,et al.  Extreme value statistics of wind speed data by the ACER method , 2013 .

[93]  E. Akpinar,et al.  A statistical analysis of wind speed data used in installation of wind energy conversion systems , 2005 .

[94]  Francisco G. Montoya,et al.  Renewable energy production in Spain: A review , 2014 .

[95]  Azami Zaharim.  Plenary lecture 9: analyzing Malaysian wind speed data using statistical distribution , 2009 .

[96]  E. Akpinar,et al.  ESTIMATION OF WIND ENERGY POTENTIAL USING FINITE MIXTURE DISTRIBUTION MODELS , 2009 .

[97]  Hang Qu,et al.  Wind power in China--Opportunity goes with challenge , 2010 .