A correction to the unimodal and bimodal truncated normal distributions for a more accurate representation of extreme and calm wind speeds. (10th September 2019) - Mazzeo, Domenico; Oliveti, Giuseppe; Marsico, Alberta
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 R 2 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. Abstract : A correction to the two‐parameter truncated normal distribution and five‐parameter mixture of two truncated normal distributions is proposed for a more accurate representation of unimodal or bimodal shapes at the centre wind speeds, calm wind speeds, and extreme wind speeds simultaneously. Analytical expressions of the mean, mean square, and mean cubic wind speed of these distributions, employed in the wind energy availability determination in a locality, were obtained and validated using the numerical integration method. Accuracy of these distributions was compared with that of the most common unimodal and bimodal distributions by using different goodness‐of‐fit (GOF) test and by calculating errors in the determination of the characteristics mean wind speeds in some Italian and American meteorological stations.