Principal Component Density Estimation for Scenario Generation Using Normalizing Flows

arXiv (Cornell University)

Abstract

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 to 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 data set, time series, or otherwise, which can be efficiently reduced using PCA.

Authors 4

1. Eike Cramer Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Forschungszentrum Jülich GmbH , Institute of Energy and Climate Research , Energy Systems Engineering (IEK- 10) , Jülich 52425 , Germany

   RWTH Aachen University Aachen 52062 , Germany

2. Alexander Mitsos
3. Raul F. Tempone Aachen Institute of Uncertainty Quantification

   King Abdullah University of Science and Technology · RWTH Aachen University

   Affiliation as printed

   King Abdullah University of Science and Technology (KAUST) , Computer, Electrical, and Mathematical Sciences & Engineering Division (CEMSE) , Saudi Arabia

   RWTH Aachen University , Institute of Uncertainty Quantification , Aachen 52062 , Germany

4. Manuel Dahmen

   Forschungszentrum Jülich

   Affiliation as printed

   Forschungszentrum Jülich GmbH , Institute of Energy and Climate Research , Energy Systems Engineering (IEK- 10) , Jülich 52425 , Germany