Principal component density estimation for scenario generation using normalizing flows

Eike Cramer, Alexander Mitsos, Raúl Tempone, Manuel Dahmen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Neural networks-based learning of the distribution of non-dispatchable renewable electricity generation from sources, such as photovoltaics (PV) and wind as well as load demands, has recently gained attention. Normalizing flow density models are particularly well suited for this task due to the training through direct log-likelihood maximization. However, research from the field of image generation has shown that standard normalizing flows can only learn smeared-out versions of manifold distributions. Previous works on normalizing flow-based scenario generation do not address this issue, and the smeared-out distributions result in the sampling of noisy time series. In this paper, we exploit the isometry of the principal component analysis (PCA), which sets up the normalizing flow in a lower-dimensional space while maintaining the direct and computationally efficient likelihood maximization. We train the resulting principal component flow (PCF) on data of PV and wind power generation as well as load demand in Germany in the years 2013-2015. The results of this investigation show that the PCF preserves critical features of the original distributions, such as the probability density and frequency behavior of the time series. The application of the PCF is, however, not limited to renewable power generation but rather extends to any dataset, time series, or otherwise, which can be efficiently reduced using PCA.

Original languageEnglish (US)
Article numbere7
JournalData-Centric Engineering
Issue number1-3
StatePublished - Mar 25 2022


  • Dimensionality reduction
  • normalizing flows
  • principal component analysis
  • renewable energy
  • scenario generation

ASJC Scopus subject areas

  • Statistics and Probability
  • General Engineering
  • Computer Science Applications
  • Applied Mathematics


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