Estimation of wind speed probability density function using a mixture of two truncated normal distributions. (January 2018) - Mazzeo, Domenico; Oliveti, Giuseppe; Labonia, Ester
Abstract: Probability density functions (PDFs) are normally used to describe wind speed distribution for the proper selection of wind turbines in a given location. The identification of a suitable PDF is fundamental for accurately assessing the wind energy potential and designing the wind farms. To achieve this objective, the use of a mixture of two truncated normal distributions (MTTND), defined for v ≥ 0 and obtained by linearly combining two normal distributions with different means and variances, is proposed in this work for the representation of the wind speed PDF. The distribution is a function of five parameters, does not require a high computational burden and allows the representation of wind calm hours (v = 0). The use of the MTTND allows an accurate estimation to be obtained of the experimental discrete distribution of the probability density and cumulative probability, and the characteristic statistical quantities used to estimate the available energy and the performance indicators in the selection of both the site and wind turbine. The validity of the use of the MTTND was verified by comparison with the most widespread PDFs in the scientific literature: Weibull, Rayleigh, lognormal, gamma, inverse Gaussian and Burr. This comparison was developed using experimental wind speed data relating to five Italian locations and a location in Colorado (USA) belonging to the National Renewable Energy Laboratory. For each location, the parameters of each PDF were obtained with the least squares non-linear regression method. The results of the comparisons, in terms of the coefficient of determination R 2 and root mean square error (RMSE) for goodness of fit and in terms of relative error in the calculation of the statistical quantities, show that the use of the MTTND gives rise to greater accuracy than a conventional wind speed PDF. Highlights: A mixture of two truncated normal distributions representing wind speed is proposed. Analytical expressions of the various statistical quantities were obtained. The MTTND was compared with the most widespread distributions in the literature. The wind speed data of five Italian locations and a location in Colorado were used. The statistical evaluations obtained by using the MTTND are more accurate.