Using Vine Copulas to Generate Representative System States for Machine Learning

Abstract

The increasing uncertainty that surrounds electricity system operation renders security assessment a highly challenging task; the range of possible operating states expands, rendering traditional approaches based on heuristic practices and ad hoc analysis obsolete. In turn, machine learning can be used to construct surrogate models approximating the system's security boundary in the region of operation. To this end, past system history can be useful for generating anticipated system states suitable for training. However, inferring the underlying data model, to allow high-density sampling, is problematic due to the large number of variables, their complex marginal probability distributions and the nonlinear dependence structure they exhibit. In this paper, we adopt the C-Vine pair-copula decomposition scheme; clustering and principal component transformation stages are introduced, followed by a truncation to the pairwise dependency modeling, enabling efficient fitting and sampling of large datasets. Using measurements from the French grid, we show that a machine learning training database sampled from the proposed method can produce binary security classifiers with superior predictive capability compared to other approaches.