Normalizing flow-based scenario generation for energy system optimization

  • Normalizing Flow basierte Szenario Generierung für Energiesystemoptimierung

Cramer, Eike Casjen Friedrich; Mitsos, Alexander (Thesis advisor); Witthaut, Dirk (Thesis advisor)

Aachen : RWTH Aachen University (2022)
Book, Dissertation / PhD Thesis

In: Aachener Verfahrenstechnik Series AVT.SVT - Process Systems Engineering 29 (2022)
Page(s)/Article-Nr.: 1 Online-Ressource : Illustrationen, Diagramme

Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2022


The electricity supply for intense power processes is shifting towards renewable sources, and, thus, operators must deal with the inherent uncertainty of photovoltaic and wind turbine power generation. Numerical optimization problems for energy system design and short-term production scheduling can be formulated by considering scenarios of uncertain parameters using stochastic programming formulations. This thesis uses the normalizing flow DGM to derive a complete end-to-end approach to generate high-quality scenarios that represent the actual distributions accurately and, thus, lead to profitable decisions in the subsequent stochastic program. For a basis for the latter evaluation, this thesis performs a critical assessment of the validation methods used in the DGM-based scenario generation literature. The standard normalizing flow design prohibits learning the distributions of data sets on lower-dimensional manifolds. Since electricity time series typically have strong autocorrelations, whole interval vectors typically follow manifold distributions. This thesis proposes an approach based on manifold learning that alleviates the issues associated with training normalizing flows on time series data. In particular, isometric embeddings are used as they do not distort the distributions and, thus, allow for a separation of the manifold learning and the normalizing flow training. The resulting composition of isometries and normalizing flows is used to learn the distributions of renewable power generation and electricity demands. Normalizing flows seamlessly incorporate external information and allow the user to train powerful and flexible scenario generation models that generate vectors of time series intervals. This thesis uses the conditional normalizing flows for day-ahead scenario generation and probabilistic forecasts of intraday electricity prices. Compared to historical data and other scenario generation methods, the normalizing flow-based day-ahead scenarios achieve the highest profits and are consistently closest to the perfect foresight solution. Furthermore, the conditional normalizing flow results in reliable and sharp probabilistic forecasts of intraday electricity prices.


  • Chair of Process Systems Engineering [416710]