Using Vine Copulas to Generate Representative System States for Machine Learning

Ioannis Konstantelos, Mingyang Sun, Simon Tindemans, Samir Issad, Patrick Panciatici, Goran Strbac

Research output: Contribution to journalArticleScientificpeer-review

23 Citations (Scopus)
363 Downloads (Pure)


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.

Original languageEnglish
Article number8418852
Pages (from-to)225-235
Number of pages11
JournalIEEE Transactions on Power Systems
Issue number1
Publication statusPublished - 2019

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project

Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Copulas
  • data clustering
  • machine learning
  • Monte Carlo simulation
  • parametric statistics
  • principal component analysis
  • risk assessment
  • stochastic dependence
  • uncertainty analysis


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