Wind speed analysis using the Extended Generalized Lindley Distribution

Kantar, Yeliz Mert; Usta, İlhan; Arik, Ibrahim; Yenılmez, İsmail

doi:10.1016/j.renene.2017.09.053

Cited by 48 publications

(22 citation statements)

References 27 publications

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“…The B3D and W2D have the most asymmetric error distributions with IQR 12 << IQR 23 , while the W2TND, W2W2D, W2B3D, and TNB3D have the most asymmetric error distributions with IQR 23 << IQR 12 . W2D and CTND can lead to an underestimation or overestimation of the mean wind speed.…”

Section: Relative Error Of the Mean Wind Speedmentioning

confidence: 99%

“…10 Recently, Alavi et al studied the performance of Nakagami distribution against some previously used PDFs including exponential, Weibull, gamma, lognormal, loglogistic, inverse normal, and generalized extreme value in Iran. 12 Similarly, Weibull, gamma, inverse normal, lognormal, Gumbel, generalized extreme value, Nakagami, and generalized logistic distribution were directly compared in Algeria. 12 Similarly, Weibull, gamma, inverse normal, lognormal, Gumbel, generalized extreme value, Nakagami, and generalized logistic distribution were directly compared in Algeria.…”

Section: Single and Mixture Distributionsmentioning

confidence: 99%

“…Replacing Equation (10) into Equation (8) and by solving the integral, the CDF equation is obtained, Equation (12).…”

Section: Corrected Truncated Normal Distribution (Ctnd) Pdf and Cdfmentioning

confidence: 99%

“…The distance between the first and the second quartile IQR 12 and that between the second and the third quartile IQR 23 allow the identification if the error distribution is symmetric. For this reason, a box plot representation of the relative error was used.…”

Section: Table 4 (Continued)mentioning

confidence: 99%

“…11 Instead, in another study, the extended generalized Lindley distribution was proposed and evaluated to show its capability in estimating wind speed data in different regions of Turkey compared with the Weibull, Rayleigh, lognormal, and gamma distributions. 12 Similarly, Weibull, gamma, inverse normal, lognormal, Gumbel, generalized extreme value, Nakagami, and generalized logistic distribution were directly compared in Algeria. 13 Masseran proposed an integrated rank approach in determining the best model selection for wind speed data.…”

Section: Single and Mixture Distributionsmentioning

confidence: 99%

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A correction to the unimodal and bimodal truncated normal distributions for a more accurate representation of extreme and calm wind speeds

2019

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Summary The use of wind speed probability density functions is a standard practice to represent different wind regimes. Generally, these regimes are distinguished by the following three characteristics: the shape of the distribution in the central wind speeds, amount of the calm wind speeds (CWS), and extreme wind speeds (EWS). An in‐depth review has highlighted that none of the parametric distributions available is suitable to represent the three main characteristics at the same time. To overcome this gap, the use of the corrected mixture of two truncated normal distributions (CMTTND) and corrected single truncated normal distribution (CTND) are proposed to represent, respectively, bimodal and unimodal wind speed distribution shapes. The CMTTND and CTND are obtained by introducing a correction, respectively, to the mixture of two truncated normal distributions (MTTND) and to the single truncated normal distribution (TND). The MTTND and TND permit an accurate representation of distributions with high levels of CWS. The CMTTND and CTND employ a new parameter, to accurately quantifying also the relative frequencies associated with EWS. The performance of the CMTTND and CTND was assessed using a goodness‐of‐fit (GOF) test and statistical measures of error in the evaluation of the characteristic mean wind speeds. The analytical expressions of these mean wind speeds are obtained and validated by a numerical integration method for the first time in this work. The accuracy of these distributions is compared with that of other conventional probability distribution models, of which three are unimodal and six bimodal, in four Italian locations and three American locations. The analysis of the results showed that the CTND and CMTTND allow obtaining high GOF of the experimental distributions with R2 and RMSE higher and lower than, respectively, 0.977 and 0.054. Moreover, the CTND results in the most accurate distribution in the estimation of the characteristic mean wind speeds in the case of localities with unimodal experimental distributions and the CMTTND in the case of localities with bimodal experimental distributions. Contrary to other distribution, CTND and CMTTND accuracies grow by increasing the grade of the characteristic mean wind speed by reaching also estimation values lower than 2% of the real ones. This is a great advantage in the wind energy source determination in a location since the available energy depends on the mean cubic wind speed.

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Section: Relative Error Of the Mean Wind Speedmentioning

confidence: 99%