A Direct Index 1 DAE Model of Gas Networks

Chapter

Abstract

Using isothermal Euler equations and a network graph to model gas flow in a pipeline network is a classical description, and we prove that any direct space discretization results in a system of index 2 nonlinear differential algebraic equations (DAE). Those are hard to simulate, and model order reduction techniques are not very developed for this system class. However, we can show that a simple approximation results in an index 1 system of nonlinear differential algebraic equations, which is easier to simulate and we can show that a structured projection leads to a reduced system that also typically has index 1. We validate the use of this model and its advantage for fast simulation, including model order reduction, in some numerical examples.

Notes

Acknowledgements

Financial support by the German Ministry of Economics (BMWi) within the Project MathEnergy, FKZ 03240198, within the research network energy system analysis (Energiesystemanalyse), is gratefully acknowledged. Responsibility for the contents of this paper rests with the authors.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Peter Benner
    • 1
  • Maike Braukmüller
    • 2
  • Sara Grundel
    • 1
  1. 1.Max Planck Institute for Dynamics of Complex Technical SystemsMagdeburgGermany
  2. 2.Institute Computational Mathematics TU BraunschweigBraunschweigGermany

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