Evaluation of bivariate Archimedean and elliptical copulas to model wind power dependency structures

Abstract

When modeling wind power from several sources, consideration of the dependency structure of the sources is of critical importance. Failure to appropriately account for the dependency structure can lead to unrealistic models, which may result in erroneous conclusions from wind integration studies and other analyses. The dependency structure is fully described by the multivariate joint distribution function of the wind power. However, fewif anyexplicit joint distribution models of wind power exist. Instead, copulas can be used to create joint distribution functions, provided that the selected copula family reasonably approximates the dependency structure. Unfortunately, there is little guidance on which copula family should be used to model wind power. The purpose of this paper is to investigate which copula families are best suited to model wind power dependency structures. Bivariate copulas are considered in particular. The paper focuses on power from wind plantscollections of wind turbines with a common interconnection pointbut the methodology can be generally extended to consider power from individual wind turbines or even aggregate wind power from entire systems. Twelve Archimedean and elliptical copulas are evaluated using hourly data from 500 wind plant pairs in the National Renewable Energy Laboratory's Eastern Dataset. The evaluation is based on (2) and Cramer-von Mises statistics. Application guidelines recommending which copula family to use are developed. It is shown that a default assumption of Gaussian dependence is not justified and that the use of Gumbel copulas can result in improved models. An illustrative example shows the application of the guidelines to model dependence of wind power sources in Monte Carlo simulations. Copyright (c) 2012 John Wiley & Sons, Ltd.