  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 have performed particularly well in 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 and can result in the
generation of noisy data. To avoid the generation of time series data with
unrealistic noise, we propose a dimensionality-reducing flow layer based on the
linear principal component analysis (PCA) that sets up the normalizing flow in
a lower-dimensional space. 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.
