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 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.

Application of differential evolution for wind speed distribution parameters estimation

2021 ◽  
pp. 0309524X2199996
Author(s):  
Rajesh Kumar ◽  
Arun Kumar
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Wind Speed ◽  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Speed Distribution ◽  
De Algorithm ◽  
Wind Speed Distribution ◽  
Distribution Parameters

Weibull distribution is an extensively used statistical distribution for analyzing wind speed and determining energy potential studies. Estimation of the wind speed distribution parameter is essential as it significantly affects the success of Weibull distribution application to wind energy. Various estimation methods viz. graphical method, moment method (MM), maximum likelihood method (ML), modified maximum likelihood method, and energy pattern factor method or power density method have been presented in various reported research studies for accurate estimation of distribution parameters. ML is the most preferred approach to study the parameter estimation. ML works on the principle of forming a likelihood function and maximizing the function for parameter estimation. ML generally uses the numerical based iterative method, such as Newton–Raphson. However, the iterative methods proposed in the literature are generally computationally intensive. In this paper, an efficient technique utilizing differential evolution (DE) algorithm to enhance the estimation accuracy of maximum likelihood estimation has been presented. The [Formula: see text] of GA-Weibull, SA-Weibull, and DE-Weibull is 0.958, 0.953, and 0.973 respectively, and value of RMSE of DE-Weibull 0.0083, GA-Weibull (0.0104), and SA-Weibull (0.0110), for the yearly wind speed data are obtained. The lowest root mean square error and larger regression value for both monthly and yearly wind speed data indicate that the DE-Weibull distribution has the best goodness of fit and advocate the DE algorithm for the parameter estimation.

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.

Comparison of Three Methods for Weibull Distribution in Calculating Wind Energy Potential

2014 ◽  
Vol 492 ◽  
pp. 574-578 ◽  
Author(s):  
Razika Ihaddadene ◽  
Nabila Ihaddadene ◽  
Merouane Mostefaoui
Keyword(s):  
Wind Speed ◽  
Wind Energy ◽  
Weibull Distribution ◽  
Failure Analysis ◽  
Power Density ◽  
Moment Method ◽  
Ground Level ◽  
Coefficient Of Determination ◽  
Energy Potential ◽  
The Moment

Three kinds of methods commonly used for estimating Weibull parameters were fitted to a collection of wind speed data at 10 m above ground level for the year of 2009 to determine the best distribution function which describes the wind speed variation at Msila, Algeria site for wind energy. Three methods used the coefficient of determination R2, root mean square error RMSE and Chi-Square χ2 were compared with failure analysis. According to the results of failure analysis the moment method has better results than graphic method and power density method. The wind power density calculated from moment method shows a good approximation to estimate the power density. So the Weibull distribution using the moment method adequately fit the data and it is suitable for modeling the wind speed distribution in Msila province of Algeria.

Analysis of wind speed data and wind energy potential in Faya-Largeau, Chad, using Weibull distribution

2018 ◽  
Vol 121 ◽  
pp. 1-8 ◽  
Author(s):  
M.H. Soulouknga ◽  
S.Y. Doka ◽  
N.Revanna ◽  
N.Djongyang ◽  
T.C.Kofane
Keyword(s):  
Wind Speed ◽  
Wind Energy ◽  
Weibull Distribution ◽  
Energy Potential ◽  
Wind Speed Data ◽  
Wind Energy Potential

scholarly journals Selection of Efficient Parameter Estimation Method for Two-Parameter Weibull Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Mohammed M. A. Almazah ◽  
Muhammad Ismail
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Estimation Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Mean Square ◽  
Two Parameter

Several studies have considered various scheduling methods and reliability functions to determine the optimum maintenance time. These methods and functions correspond to the lowest cost by using the maximum likelihood estimator to evaluate the model parameters. However, this paper aims to estimate the parameters of the two-parameter Weibull distribution (α, β). The maximum likelihood estimation method, modified linear exponential loss function, and Wyatt-based regression method are used for the estimation of the parameters. Minimum mean square error (MSE) criterion is used to evaluate the relative efficiency of the estimators. The comparison of the different parameter estimation methods is conducted, and the efficiency of these methods is observed, both mathematically and experimentally. The simulation study is conducted for comparison of samples sizes (10, 50, 100, 150) based on the mean square error (MSE). It is concluded that the maximum likelihood method was found to be the most efficient method for all sample sizes used in the research because it achieved the least MSE compared with other methods.

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