Using Copulas for Modeling Stochastic Dependence in Power System Uncertainty Analysis

TLDR

The increasing penetration of renewable generation creates multivariate uncertainty with non‑normal, correlated random variables, making accurate modeling of stochastic dependence essential for reliable system analysis. The study presents the basic theory of copula‑based dependence modeling, concentrating on the Normal copula. The authors transform all random variables to a common rank/uniform domain via their cumulative distribution functions and then use copula functions—specifically the Normal copula—to capture stochastic dependence. A case study demonstrates the technique’s application to evaluate large‑scale wind power integration in the Netherlands.

Abstract

The increasing penetration of renewable generation in power systems necessitates the modeling of this stochastic system infeed in operation and planning studies. The system analysis leads to multivariate uncertainty analysis problems, involving non-Normal correlated random variables. In this context, the modeling of stochastic dependence is paramount for obtaining accurate results; it corresponds to the concurrent behavior of the random variables, having a major impact to the aggregate uncertainty (in problems where the random variables correspond to spatially spread stochastic infeeds) or their evolution in time (in problems where the random variables correspond to infeeds over specific time-periods). In order to investigate, measure and model stochastic dependence, one should transform all different random variables to a common domain, the rank/uniform domain, by applying the cumulative distribution function transformation. In this domain, special functions, copulae, can be used for modeling dependence. In this contribution the basic theory concerning the use of these functions for dependence modeling is presented and focus is given on a basic function, the Normal copula. The case study shows the application of the technique for the study of the large-scale integration of wind power in the Netherlands.