Principal Component Density Estimation for Scenario Generation Using Normalizing Flows

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.