Evaluating Archimedean Copula models of wind speed for wind power modeling

Copula theory presents a viable method of modeling dependence structures of random variables when their joint distribution function is not explicitly known. Copulas can be applied to model the wind speed at wind plants, which can be transformed to wind power and used in simulations. As with any application of parametric copulas, the user must decide which copula family to use, and how to select its parameters. The purpose of this paper is to evaluate the fit of a popular class of copulas-Archimedean Copulas-to model wind speed dependence. It is proposed that the selection of the copula´s parameters be done to achieve a user-specified rank correlation. The determination of appropriate rank correlation coefficients is guided through a developed distance-of-separation dependent rank correlation model of wind speed. Data from the National Renewable Energy Laboratory´s Eastern Dataset are used to develop the models and evaluate the fit of the copulas. It is shown that the Gumbel Archimedean copula family is the best-suited for wind speed dependence structure modeling.