Polynomial Chaos Approach to Describe the Propagation of Uncertainties Through Gas Networks

  • Stephan GersterEmail author
  • Michael Herty
  • Michael Chertkov
  • Marc Vuffray
  • Anatoly Zlotnik
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)


The ability of gas-fired power plants to ramp quickly is used to balance fluctuations in the power grid caused by renewable energy sources, which in turn leads to time-varying gas consumption and fluctuations in the gas network. Since gas system operators assume nearly constant gas consumption, there is a need to assess the risk of these stochastic fluctuations, which occur on shorter time scales than the planning horizon. We present a mathematical formulation for these stochastic fluctuations as a generalization of isothermal Euler equations. Furthermore, we discuss control policies to damp fluctuations in the network.


Gas networks Hyperbolic partial differential equations Uncertainty quantification Stochastic Galerkin method Polynomial chaos expansion 



This work is supported by DFG HE5386/14,15, BMBF 05M18PAA, DFG-GRK 2326, Student Guest Program of Los Alamos National Laboratory.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Stephan Gerster
    • 1
    Email author
  • Michael Herty
    • 1
  • Michael Chertkov
    • 2
  • Marc Vuffray
    • 2
  • Anatoly Zlotnik
    • 2
  1. 1.IGPMRWTH Aachen UniversityAachenGermany
  2. 2.CNLSLos Alamos National LaboratoryLos AlamosUSA

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