Model Order Reduction for Gas and Energy Networks

Christian Himpe, Sara Grundel, Peter Benner

To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these new circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query task can be accelerated by model order reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential (-algebraic) equation systems, modeling gas transport, are a challenging application for model reduction algorithms. For this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and model order reduction for nonlinear parametric systems. This research resulted in the "morgen" (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of "morgen" and associated numerical experiments testing model reduction adapted to gas network models.

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