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Optimization and Engineering

, Volume 20, Issue 2, pp 543–573 | Cite as

Maximizing the storage capacity of gas networks: a global MINLP approach

  • Robert BurlacuEmail author
  • Herbert Egger
  • Martin Groß
  • Alexander Martin
  • Marc E. Pfetsch
  • Lars Schewe
  • Mathias Sirvent
  • Martin Skutella
Research Article

Abstract

In this paper, we study the transient optimization of gas networks, focusing in particular on maximizing the storage capacity of the network. We include nonlinear gas physics and active elements such as valves and compressors, which due to their switching lead to discrete decisions. The former is described by a model derived from the Euler equations that is given by a coupled system of nonlinear parabolic partial differential equations (\({\text{PDEs}}\)). We tackle the resulting mathematical optimization problem by a first-discretize-then-optimize approach. To this end, we introduce a new discretization of the underlying system of parabolic \({\text{PDEs}}\) and prove well-posedness for the resulting nonlinear discretized system. Endowed with this discretization, we model the problem of maximizing the storage capacity as a non-convex mixed-integer nonlinear problem (\({\text{MINLP}}\)). For the numerical solution of the \({\text{MINLP}}\), we algorithmically extend a well-known relaxation approach that has already been used very successfully in the field of stationary gas network optimization. This method allows us to solve the problem to global optimality by iteratively solving a series of mixed-integer problems. Finally, we present two case studies that illustrate the applicability of our approach.

Keywords

Mixed-integer nonlinear programming Transient gas transport optimization Storage capacity maximization Power-to-gas First-discretize-then-optimize 

Notes

Acknowledgements

The authors gratefully acknowledge the compute resources and support provided by the Erlangen Regional Computing Center (RRZE). We are very grateful for the thorough reading of the paper by Martin Schmidt. We would also like to show our gratitude to Fabian Rüffler for fruitful discussions on the topic of discretization of \({\text{PDEs}}\). Finally, we thank Falk Hante for his helpful comments on the literature review of the general approaches for optimal control with discrete decisions.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Discrete OptimizationFriedrich-Alexander-Universität Erlangen-Nürnberg (FAU)ErlangenGermany
  2. 2.Research Group Numerics and Scientific ComputingTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Chair of Management ScienceRWTH AachenAachenGermany
  4. 4.Research Group OptimizationTechnische Universität DarmstadtDarmstadtGermany
  5. 5.Faculty II – Mathematics and Natural SciencesTechnische Universität BerlinBerlinGermany

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