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High detail stationary optimization models for gas networks: validation and results

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Abstract

Due to strict regulatory rules in combination with complex nonlinear physics, major gas network operators in Germany and Europe face hard planning problems that call for optimization. In part 1 of this paper we have developed a suitable model hierarchy for that purpose. Here we consider the more practical aspects of modeling. We validate individual model components against a trusted simulation tool, give a structural overview of the model hierarchy, and use its large variety of approximations to devise robust and efficient solution techniques. An extensive computational study demonstrates the suitability of our models and techniques for previously unsolvable problems in gas network planning.

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Notes

  1. SIMONE software. http://www.liwacom.de.

  2. https://www.open-grid-europe.com.

  3. General Algebraic Modeling System (GAMS). http://www.gams.com/.

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Acknowledgments

This work has been supported by the German Federal Ministry of Economics and Technology owing to a decision of the German Bundestag. The responsibility for the content of this publication lies with the authors. This research has been performed as part of the Energie Campus Nürnberg and supported by funding through the “Aufbruch Bayern (Bavaria on the move)” initiative of the state of Bavaria. We would also like to thank our industry partner Open Grid Europe GmbH and the project partners in the ForNe consortium. Finally, we thank Björn Geißler and Antonio Morsi for many suggestions for improvement.

Author information

Authors and Affiliations

  1. Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany

    Martin Schmidt

  2. Energie Campus Nürnberg, Fürther Str. 250, 90429, Nuremberg, Germany

    Martin Schmidt

  3. Institute for Applied Mathematics, Leibniz Universiät Hannover, Welfengarten 1, 30167, Hannover, Germany

    Marc C. Steinbach

  4. Ronnenberg, Germany

    Bernhard M. Willert

Authors
  1. Martin Schmidt
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  2. Marc C. Steinbach
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  3. Bernhard M. Willert
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Corresponding author

Correspondence to Martin Schmidt.

Appendices

Appendix 1: Computational results for temperature dynamics on the GasLib-582 test set

See Figs. 15 and 16.

Fig. 15
figure 15

Constraint violations of direct approach and of SNLP sequence

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Fig. 16
figure 16

Iteration counts and computing times (s) of direct approach and of SNLP sequence

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Appendix 2: Model aspect graphs

See Figs. 17, 18, 19, 20, and 21.

Fig. 17
figure 17

Model aspect graph of nodes (global aspect: mixing of gas types). The nodes in the shaded block exist only in non-isothermal models

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Fig. 18
figure 18

Model aspect graph of nodes (global aspect: uniform gas composition). The nodes in the shaded block exist only in non-isothermal models

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Fig. 19
figure 19

Model aspect graph of control valves. The nodes in shaded blocks exist only in non-isothermal models

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Fig. 20
figure 20

Model aspect graph of pipes (isothermal). (*) If the exact solutions of the momentum equation are chosen as a concretization, not every choice of the compressibility factor is possible, cf.  Schmidt et al. (2014). In addition, not every combination of pipe slope and compressibility factor is possible. (o) To achieve a smooth NLP model, flow bound strengthening has to be applied. (+) Only possible for horizontal pipes

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Fig. 21
figure 21

Model aspect graph of pipes (non-isothermal)

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Appendix 3: GasLib-582 instances

See Table 13.

Table 13 ID’s of GasLib-582 instances used in the computational study of Sect. 5.4. The set of instances can also be downloaded at www.ifam.uni-hannover.de/mcs
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Schmidt, M., Steinbach, M.C. & Willert, B.M. High detail stationary optimization models for gas networks: validation and results. Optim Eng 17, 437–472 (2016). https://doi.org/10.1007/s11081-015-9300-3

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  • DOI: https://doi.org/10.1007/s11081-015-9300-3

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