Using copulas for modeling stochastic dependence in power system uncertainty analysis

Using copulas for modeling stochastic dependence in power system uncertainty analysis

Papaefthymiou, G.
Kurowicka, D.

Electrical Engineering, Mathematics and Computer Science

Electrical Sustainable Energy

2009-01-23

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.

copula
correlation
Monte Carlo simulation
stochastic dependence
stochastic generation
uncertainty analysis
wind power

http://resolver.tudelft.nl/uuid:95f1600f-1d5f-4bc3-82ee-89dd490a12ba

https://doi.org/10.1109/TPWRS.2008.2004728

IEEE

0885-8950

IEEE Transactions on Power Systems, 24 (1), 2009

Institutional Repository

journal article

(c) 2009 Papaefthymiou, G.; Kurowicka, D.; IEEE