Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application

Abstract

Two-parameter Weibull function has been widely applied to evaluate wind energy potential. In this paper, six kinds of numerical methods commonly used for estimating Weibull parameters are reviewed; i.e. the moment, empirical, graphical, maximum likelihood, modified maximum likelihood and energy pattern factor method. Their performance is compared through Monte Carlo simulation and analysis of actual wind speed according to the criterions such as Kolmogorov–Smirnov test, parameter error, root mean square error, and wind energy error. The results show that, in simulation test of random variables, the graphical method’s performance in estimating Weibull parameters is the worst one, followed by the empirical and energy pattern factor methods, if data number is smaller. The performance for all the six methods is improved while data number becomes larger; the graphical method is even better than the empirical and energy pattern factor methods. The maximum likelihood, modified maximum likelihood and moment methods present relatively more excellent ability throughout the simulation tests. From analysis of actual data, it is found that if wind speed distribution matches well with Weibull function, the six methods are applicable; but if not, the maximum likelihood method performs best followed by the modified maximum likelihood and moment methods, based on double checks including potential energy and cumulative distribution function.