scholarly journals Two Improved Mixture Weibull Models for the Analysis of Wind Speed Data

2012 ◽  
Vol 51 (7) ◽  
pp. 1321-1332 ◽  
Author(s):  
Xu Qin ◽  
Jiang-she Zhang ◽  
Xiao-dong Yan
Keyword(s):  
Wind Speed ◽  
Weibull Distribution ◽  
Likelihood Method ◽  
Distribution Models ◽  
Component Mixture ◽  
Wind Speed Data ◽  
Two Component ◽  
Weibull Models ◽  
Improved Model ◽  
Two Parameter

AbstractIn this paper, the authors propose two improved mixture Weibull distribution models by adding one or two location parameters to the existing two-component mixture two-parameter Weibull distribution [MWbl(2, 2)] model. One improved model is the mixture two-parameter Weibull and three-parameter Weibull distribution [MWbl(2, 3)] model. The other improved model is the two-component mixture three-parameter Weibull distribution [MWbl(3, 3)] model. In contrast to existing literature, which has focused on the MWbl(2, 2) and the typical Weibull distribution models, the authors apply the MWbl(2, 3) model and MWbl(3, 3) model to fit the distribution of wind speed data with nearly zero percentages of null wind speed. The parameters of the two improved models are estimated by the maximum likelihood method in which the maximization problem is regarded as a nonlinear programming problem with only inequality constraints and is solved numerically by the interior-point method. The experimental results show that the mixture Weibull models proposed in this paper are more flexible than the existing models for the analysis of wind speed data in practice.

scholarly journals Performance Comparison of New Generation Parameter Estimation Methods for Weibull Distribution to Compute Wind Energy Density

2021 ◽  
Author(s):  
Ahmet Emre Onay ◽  
Emrah Dokur ◽  
Mehmet Kurban
Keyword(s):  
Parameter Estimation ◽  
Wind Speed ◽  
Wind Energy ◽  
Weibull Distribution ◽  
Performance Metrics ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Coefficient Of Determination ◽  
Wind Speed Data ◽  
Parameter Estimation Methods

To install a wind energy conversion system to a region, the wind speed characteristics of that region must be identified. The two-parameter Weibull distribution is highly efficient in modeling wind speed characteristics. In this study, the wind speed data of 32 cities in three different regions of Turkey have been comparatively analysed to estimate Weibull distribution function parameters by the use of three well-known methods (Graphical Method (GM), Maximum Likelihood Method (MLM), Justus Moment Method (JMM)) and three new parameter estimation methods (Energy Pattern Factor Method (EPFM), Wind Energy Intensification Method (WEIM), Power Density Method (PD)) which have been proposed in recent years. Three years of hourly wind speed data of the specified regions have been used. The performance metrics of these analyses have been compared using Wind Energy Error (WEE), Root Mean Square Error (RMSE), and Coefficient of Determination (R2). The results have shown that while the PD method has high model performance, the JMM is closely competitive with the MLM. Besides, the wind energy densities that were estimated by using actual data have been compared with the resulting Weibull distribution. It has been clear that the method that has the closest estimation to the actual values is the PD method.

scholarly journals Best estimation for the Reliability of 2-parameter Weibull Distribution

2009 ◽  
Vol 6 (4) ◽  
pp. 705-710
Author(s):  
Baghdad Science Journal
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Statistical Criterion ◽  
Mean Square ◽  
Simulation Process ◽  
The Mean ◽  
Two Parameter

This Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.

scholarly journals Frequency Distribution Model of Wind Speed Based on the Exponential Polynomial for Wind Farms

2019 ◽  
Vol 11 (3) ◽  
pp. 665 ◽  
Author(s):  
Lingzhi Wang ◽  
Jun Liu ◽  
Fucai Qian
Keyword(s):  
Wind Speed ◽  
Frequency Distribution ◽  
Least Squares Method ◽  
Wind Farms ◽  
Rayleigh Distribution ◽  
Distribution Model ◽  
Exponential Polynomial ◽  
Distribution Models ◽  
Wind Speed Data ◽  
Wind Speeds

This study introduces and analyses existing models of wind speed frequency distribution in wind farms, such as the Weibull distribution model, the Rayleigh distribution model, and the lognormal distribution model. Inspired by the shortcomings of these models, we propose a distribution model based on an exponential polynomial, which can describe the actual wind speed frequency distribution. The fitting error of other common distribution models is too large at zero or low wind speeds. The proposed model can solve this problem. The exponential polynomial distribution model can fit multimodal distribution wind speed data as well as unimodal distribution wind speed data. We used the linear-least-squares method to acquire the parameters for the distribution model. Finally, we carried out contrast simulation experiments to validate the effectiveness and advantages of the proposed distribution model.

Analyzing wind speed data and wind power density of Tetouan city in Morocco by adjustment to Weibull and Rayleigh distribution functions

2017 ◽  
Vol 41 (3) ◽  
pp. 174-184 ◽  
Author(s):  
Mohamed Hatim Ouahabi ◽  
Farid Benabdelouahab ◽  
Abdellatif Khamlichi
Keyword(s):  
Wind Speed ◽  
Measurement Data ◽  
Rayleigh Distribution ◽  
Distribution Functions ◽  
Statistical Distributions ◽  
Energy Potential ◽  
Distribution Models ◽  
Wind Speed Data ◽  
Resource Characteristics ◽  
Wind Resource

Several statistical distributions have been considered to model wind speed data. However, Weibull and Rayleigh statistical distributions are the most widely used methods for analyzing wind speed measurements and determining wind energy potential. In this work, these statistical distributions were applied in order to evaluate the wind resources in the northern Moroccan city of Tetouan. Adjustment of wind measurement data was performed. Then, the obtained results were compared with the provided wind data to test their accuracy based on common statistical indicators for performance. It was found that the Weibull and Rayleigh distribution models provide adequate description of the frequencies of actual wind records in Tetouan. They can be advantageously used to assess wind resource characteristics in this region.

scholarly journals Assessing the Best Fit Probability Distribution Model for Wind Speed Data for Different Sites of Burkina Faso

2020 ◽  
pp. 71-83
Author(s):  
Drissa Boro ◽  
Ky Thierry ◽  
Florent P. Kieno ◽  
Joseph Bathiebo
Keyword(s):  
Wind Speed ◽  
Weibull Distribution ◽  
Burkina Faso ◽  
Mean Absolute Error ◽  
Absolute Error ◽  
Likelihood Method ◽  
Distribution Model ◽  
Coefficient Of Determination ◽  
Inverse Gaussian ◽  
Study Sites

In order to estimate the power output of a wind turbine, optimise its sizing and forecast the economic rate of return and risks of a wind energy project, wind speed distribution modelling is crucial. For which, Weibull distribution is considered as one of the most acceptable model. However, this distribution does not fit certain wind speed regimes. The objective of this study is to model the frequency distribution of the three-hourly wind speed at ten sites of Burkina Faso. In this context, we compared the accuracy of five distributions (Weibull, Hybrid Weibull, Rayleigh, Gamma and inverse Gaussian) which gave satisfactory results in this field. The maximum likelihood method was used to fit the distributions to the measured data. According to the statistical analysis tools (the coefficient of determination and the root mean square error), it was found that the Weibull distribution is most suited to the Bobo, Dédougou, Ouaga and Ouahigouya sites. On the other hand, for the sites of Bogandé, Fada and Po, the hybrid Weibull distribution is the most suitable one. As to the inverse Gaussian distribution, it is the most suitable for the Boromo, Dori and Gaoua sites. In addition, the analysis focused on comparing the mean absolute error of the annual wind power density estimation using the distributions examined. The Hybrid Weibull distribution was found to have a minimal mean absolute error for most study sites.

A python program to model and analyze wind speed data

2021 ◽  
Vol 9 (6) ◽  
pp. 769-784
Keyword(s):  
Maximum Likelihood ◽  
Wind Speed ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Weibull Function ◽  
Method Of Moment ◽  
Wind Speed Data ◽  
Statistical Errors ◽  
Wind Potential ◽  
Wind Distribution

A python program has been developed to analyze wind distributions using the Weibull density function. A two-parameter Weibull function is frequently used to model and assess wind potential and wind distribution. This python program finds first Weibull parameters from the recorded wind data by five different methods, namely, Empirical Method(EPM), Method of Moment (MoM), Energy Pattern Factor Method (EPFM), Maximum Likelihood Method (MLM), Modified Maximum Likelihood Method (MMLM), the parameters are then used to find theoretically fitted pdfs. The program is implemented on wind distribution of two cities of Pakistan (Chakri and Sadiq Abad). The program-generated pdfs were plotted with the histogram of recorded data, the fitting was excellent. To check the validity of the fitted pdfs, statistical errors Root Mean Square (RMSE), MeanAbsolute Percent Error (MAPE), Mean Absolute Error (MABE), and Chi-square statistic are calculated. In all cases,these statistical errors are well below the acceptance range. Both pictorial results and numerical values of statistical errors indicate the performance of the python program to analyze wind speed data

scholarly journals Testing average wind speed using sampling plan for Weibull distribution under indeterminacy

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Muhammad Aslam
Keyword(s):  
Wind Speed ◽  
Weibull Distribution ◽  
Sample Size ◽  
Sampling Plan ◽  
Average Wind Speed ◽  
Wind Speed Data ◽  
Average Wind

AbstractThe time truncated plan for the Weibull distribution under the indeterminacy is presented. The plan parameters of the proposed plan are determined by fixing the indeterminacy parameter. The plan parameters are given for various values of indeterminacy parameters. From the results, it can be concluded that the values of sample size reduce as indeterminacy values increase. The application of the proposed plan is given using wind speed data. From the wind speed example, it is concluded that the proposed plan is helpful to test the average wind speed at smaller values of sample size as compared to existing sampling plan.

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