  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.
