Using Copulas for Modeling Stochastic Dependence in Power System Uncertainty Analysis

Abstract

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.

Stochastic Dual Dynamic Programming for Operation of DER Aggregators Under Multi-Dimensional Uncertainty

“…In addition, different uncertainty sources may not be independent since relationships exist between different uncertain variables, due to confounding factors such as weather conditions. In [15] for example, the authors demonstrate that ignoring the stochastic dependence characterizing the multivariate uncertainty around wind farms' output, can lead to suboptimal planning and operation decisions. In a similar vein, authors in [16] present numerous composite modeling approaches for capturing complex nonlinear dependency patterns in large power system datasets.…”

“…The problem formulation for the subsequent stages is illustrated in (15), which constitutes a generalization of (14) and symbols are used in the same context. It is assumed that the terminal cost +1 ( , +1 ) = 0, but it could be any convex function representing future costs after .…”

Wind Power System Risk Assessment Based on Fuzzy Clustering and Copula Function Modeling

“…Copula function [3] is effective in correlation problem. [4] connects copula theory with Monte Carlo simulation method for probabilistic load flow calculation.…”

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“…Their superiority lies in their ability to decouple marginal distribution from dependency modelling, rendering them well-suited to capture statistical properties of datasets that do not belong to standard multivariate distributions. For example, in [2] a multivariate Gaussian copula has been applied to generate synthetic wind power output from 15 sites in the Netherlands. A statistical modelling framework based on a multivariate Gaussian copula is also proposed in [3] to obtain complete temporal dependence structure and actual distributions of wind speed time series.…”