Power Density Method Research Articles

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

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.

Rüzgar Hızı Değerlendirmesinde İki Parametreli Weibull Dağılımı İçin Üç Parametre Tahmin Metodunun Karşılaştırmalı Performans Analizi

The two-parameter Weibull distribution is widely used in the estimation of wind speed. In this paper, some recently proposed parameter estimation methods for the two parameter Weibull distribution have been compared using the wind data from two cities in Turkey. The compared methods in this paper are Wind Energy Intensification Method (WEIM), Energy Pattern Factor Method (EPFM), and Power Density Method (PD). These methods have been compared by checking the fit have provided in the probability-density graph. The comparison has also been made by comparing of efficiencies these methods in predicting wind energy density. Lastly, a comparison has been investigated by using the following performance criteria; Wind Energy Error (WEE), Root Mean Square Error (RMSE), Coefficient of Determination (R2), and the results of error analysis have been compared. According to simulation results, while the EPFM and PD methods have shown a very close fit on the graph; when it comes to calculating wind energy densities, the PD method has shown a significant advantage over other methods. Finally, after the examination of error criteria, it was clear that EPFM has shown accurate performance which is the desired result. The main conclusion is that the accurate method for these selected regions is the EPFM.

Evaluation of weibull parameter estimators for wind speed of Jumla, Nepal

Weibull Probability Distribution Function (PDF) is widely used across world for estimation of wind power. Weibull function is a two parameter probability distribution function. The methods employed for the evaluation of these two parameters are critical for the efficient use of Weibull PDF. In the present study, three different Weibull PDF parameter estimators have been evaluated. For this purpose, the daily averaged wind speed data of Jumla Station, Nepal for period of 10 year (2004 – 2014: 2012 excluded) is studied. The parameter estimator evaluated in this study are Method of Moments (MoM), Least Square Error Method (LSEM) and Power Density Method (PDM). It has been found that Method of Moments (MoM) is the best estimator for evaluating Weibull Parameters.

Weibull parameters estimation using combined energy pattern and power density method for wind resource assessment

This work deals with the development of Combined Energy Pattern & Power Density Method (CEPPDM) to evaluate the two parameters needed to define Weibull distribution. Five years (2015–2019) wind data recorded each 60-minutes interval at eleven representative sites in Pakistan was used and efficiency of CEPPDM was compared with Energy Pattern Factor Method (EPFM) and Power Density Method (PDM) with the help of MAPE, MSE and R2. Analysis showed that CEPPDM is the most efficient method while EPFM is the least efficient. Furthermore, it was found that RYK is the most lucrative site and Layyah is the weakest site regarding wind potential. Wind rose plots were drawn which showed that the wind mainly blows in the range of 200°–270°.

Assessment of Wind Energy Prospect by Weibull Distribution for Prospective Wind Sites in Australia

In this study, three potential wind sites such as Hamilton Island, Proserpine, and South Johnstone wind speed data has been analyzed using Weibull distribution. The half-hourly time series wind speed data used in this analysis were obtained from Bureau of Meteorology, Australia wind monitoring stations. With the aim assessing the wind energy potential, method of moments (MOM), empirical method (EM), and power density method (PDM) were employed for determining the Weibull factors of the available data. The accuracy of the results was analyzed using a statistical test tool named chi-square error (χ2). The EM method was found to be the best method among the three studied methods for calculating Weibull parameters. Based on the analyzed data, a horizontal axis wind turbine specification was proposed. Finally, wind power profile of Hamilton Island site was evaluated for the proposed turbine specification.

Performance assessment of Power Density Method for determining the Weibull Distribution Coefficients at three different locations

In this study, the Weibull Distribution Function (WDF) was used for the statistical evaluation of wind potential of the southern region of Turkey. The Power Density Method (PDM) was used to calculate the parameters of the WDF. The used wind data obtained by the General Directorate of State Meteorology at 10 m above the ground in the meteorology stations located in Adana, Osmaniye and Hatay between 2009 and 2013. The performance of PDM to determine the coefficients of WDF was evaluated and compared for three different locations with different mean wind speed values. The method used was compared with such error analyses as Coefficient of Determination (R2), Mean Percentage Error (MPE) and Root Mean Square Error (RMSE). According to the results of error analysis, it was determined in which region the PDM obtained better results. Obtained data were examined on monthly, seasonal and annual bases. Therefore, in the general sense, a preliminary study was carried out with the aim of determining the wind energy potential of the southern region of Turkey. The power density is a major key issue for suitability use of wind energy. The obtained power densities of all selected regions using WDF were compared with wind power density calculated from measured wind data.

Evaluation of hydrogen production from harvesting wind energy at high altitudes in Iran by three extrapolating Weibull methods

One of the most appropriate ways for energy storage is producing hydrogen from renewable resources. Wind energy is recognized as one of the widely used renewable energy resources. This paper investigates the use of wind energy for producing hydrogen in Iran. To achieve this, the country is divided into five major regions: center, north, south, east and west. The performance of three large-scale commercial wind turbines, ranging from 1500 kW to 3000 kW at hub height of 80 m and four large-scale wind turbine ranging from 2000 kW to 4500 kW at hub height of 120 m are evaluated for producing hydrogen in 150 wind stations in Iran. All wind data were recorded based on 10-min time intervals for more than one year at different wind mast heights. For estimating Weibull parameters, the Standard Deviation Method (SDM), Empirical Method of Lysen (EML) and Power Density Method (PDM) are used. An extrapolation method is used to determine the shape and the scale parameters of the Weibull distribution at the high attitudes of 80 m and 120 m. Then, power law and surface roughness exponents, capacity factor, annual energy production and annual hydrogen production for the wind sites are determined. The results indicate that rated power is not the only determinative parameter and the highest hydrogen production is from the GW-109/2500 wind turbine at the hub height of 80 m and from E112/4500 at the hub height of 120 m. For better assessment, the amount of hydrogen production is depicted in Geographic Information Science (GIS) maps using power production of the seven wind turbine models. Next by analyzing these GIS maps, it is found that there are significant potentials in north, north-west, east and south of Iran for producing hydrogen from wind energy.

A novel energy pattern factor method for wind speed distribution parameter estimation

Power output of wind turbine depends on many factors. Among them, the most crucial one is wind speed. Since wind speed data is a significant factor for wind energy analyses, it should be modeled accurately. Weibull distribution has been used extensively to model variation of wind speed. Therefore, the most appropriate distribution parameter estimation method selection is critical in order to minimize data set modeling errors. In this context, a novel, robust, efficient and better method than standard methods to estimate Weibull parameters is presented for the first time in this paper. The accuracy of the proposed method is verified using different data sets. Also, developed method is compared with Graphic Method (GM), Maximum Likelihood Method (MLM), Alternative Maximum Likelihood Method (AMLH), Modified Maximum Likelihood Method (MMLH), Moment Method (MM), Justus Moment Method (JMM), WAsP Method (WM) and Power Density Method (PD). The results indicate that the proposed novel method is adequate to determine Weibull distribution parameters.

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.

Comparative study of four methods for estimating Weibull parameters for Halabja, Iraq

The Weibull distribution is the standard function used by the wind energy community to model the wind speed frequency distribution. In this study, four methods are presented for estimating Weibull parameters (Shape and Scale), namely, Maximum likelihood method (MLM), Rank regression method (RRM), Mean-standard deviation method (MSD), and Power density method (PDM). To compare the methods, a period of 4 years (2001 - 2004) of monthly time series data of Halabja city was considered. Two distinct analytical methods are studied to determine the parameter estimation accuracy of these methods; coefficient of determination and root mean square error (RMSE) are used as measurement tools. The Rank regression and MSDs are recommended to estimate the shape parameter; also the Rank regression is recommended for use with our time series wind data to estimate the scale parameter. Key words: Weibull distribution, parameter estimation, energy pattern factor, accuracy.