The use of wind probability distributions derived from the maximum entropy principle in the analysis of wind energy. A case study

Abstract

This paper analyses the use of a general probability distribution obtained through application of the maximum entropy principle (MEP), constrained by the low-order statistical moments of a given set of wind speed data, in the estimation of wind energy. For this purpose, a comparison is made between the two parameter Weibull distribution and the distributions obtained through the MEP. This comparison is based on an analysis of the level of fit to the cumulative frequencies of the hourly mean wind speeds recorded at weather stations located in the Canarian Archipelago. A comparison is also made of the ability to describe the experimental mean wind power density. The application of the probability plot correlation coefficient R2, adjusted for degrees of freedom, shows that the Weibull distribution, whose parameters are estimated using the maximum likelihood principle, provide worse fits in all the cases analysed than those obtained through the maximum entropy distributions constrained by the low-order statistical moments. It is, thus, shown that maximum entropy distributions constrained by the three low-order statistical moments, in addition to representing the probabilities of observed periods of null wind speeds, offer less relative errors in determining the mean wind power density than the Weibull distribution. However, among other advantages of the Weibull distribution, is the greater simplicity of the calculations involved.