Comparison of Four Distributions for Frequency Analysis of Wind Speed: A Case Study

The increase in negative effects of fossil fuels on the environment has forced many countries to use renewable energy sources, especially wind energy. Wind speed is the most important parameter of the wind energy. Probability distributions are useful for estimating wind speed because it is a random phenomenon. This study analyzes wind speed frequencies using wind data from Urmia synoptic station in Iran. Four different distributions are fitted to the maximum annual wind from station, and parameters of the distributions are estimated using the method of maximum likelihood and the method of moments. Calculations are performed with Mathematica, a computer algebra system developed by Wolfram Research. The advantage of using this software is that the symbolic, numerical, and graphical computations can be combined and that all quantities can be accurately calculated; in particular, there is no need to resort to any approximate methods for the calculation of quantiles. There is a ready-to-use command for calculating quantiles from distributions that are built in Mathematica, while for other distributions they can be easily and accurately calculated by inverting the cumulative distribution functions or by solving nonlinear equations where the inversion is not possible. The best distribution is selected based on the root mean square error (RMSE), the coefficient of determination (R2), and the probability plot correlation coefficient (PPCC). The results indicate that the best performance can be obtained by the truncated extreme value distribution.