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On the quantification of nomination feasibility in stationary gas networks with random load

Author

Listed:
  • Claudia Gotzes

    (University of Duisburg-Essen)

  • Holger Heitsch

    (Weierstrass Institute)

  • René Henrion

    (Weierstrass Institute)

  • Rüdiger Schultz

    (University of Duisburg-Essen)

Abstract

The paper considers the computation of the probability of feasible load constellations in a stationary gas network with uncertain demand. More precisely, a network with a single entry and several exits with uncertain loads is studied. Feasibility of a load constellation is understood in the sense of an existing flow meeting these loads along with given pressure bounds in the pipes. In a first step, feasibility of deterministic exit loads is characterized algebraically and these general conditions are specified to networks involving at most one cycle. This prerequisite is essential for determining probabilities in a stochastic setting when exit loads are assumed to follow some (joint) Gaussian distribution when modeling uncertain customer demand. The key of our approach is the application of the spheric-radial decomposition of Gaussian random vectors coupled with Quasi Monte-Carlo sampling. This approach requires an efficient algorithmic treatment of the mentioned algebraic relations moreover depending on a scalar parameter. Numerical results are illustrated for different network examples and demonstrate a clear superiority in terms of precision over simple generic Monte-Carlo sampling. They lead to fairly accurate probability values even for moderate sample size.

Suggested Citation

  • Claudia Gotzes & Holger Heitsch & René Henrion & Rüdiger Schultz, 2016. "On the quantification of nomination feasibility in stationary gas networks with random load," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 427-457, October.
    • Handle: RePEc:spr:mathme:v:84:y:2016:i:2:d:10.1007_s00186-016-0564-y
    DOI: 10.1007/s00186-016-0564-y
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    Citations

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    Cited by:

    1. Martina Kuchlbauer & Frauke Liers & Michael Stingl, 2022. "Outer Approximation for Mixed-Integer Nonlinear Robust Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 1056-1086, December.
    2. Zhao, Wei & Liao, Qi & Qiu, Rui & Liu, Chunying & Xu, Ning & Yu, Xiao & Liang, Yongtu, 2024. "Pipe sharing: A bilevel optimization model for the optimal capacity allocation of natural gas network," Applied Energy, Elsevier, vol. 359(C).
    3. Lars Schewe & Martin Schmidt & Johannes Thürauf, 2020. "Structural properties of feasible bookings in the European entry–exit gas market system," 4OR, Springer, vol. 18(2), pages 197-218, June.
    4. Martina Kuchlbauer & Frauke Liers & Michael Stingl, 2022. "Adaptive Bundle Methods for Nonlinear Robust Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2106-2124, July.
    5. Grimm, Veronika & Grübel, Julia & Schewe, Lars & Schmidt, Martin & Zöttl, Gregor, 2019. "Nonconvex equilibrium models for gas market analysis: Failure of standard techniques and alternative modeling approaches," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1097-1108.
    6. T. González Grandón & H. Heitsch & R. Henrion, 2017. "A joint model of probabilistic/robust constraints for gas transport management in stationary networks," Computational Management Science, Springer, vol. 14(3), pages 443-460, July.
    7. Wim Ackooij & Pedro Pérez-Aros, 2020. "Gradient Formulae for Nonlinear Probabilistic Constraints with Non-convex Quadratic Forms," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 239-269, April.
    8. Luo, Tao & Pan, Junting & Fu, Lintao & Mei, Zili & Kong, Cuixue & Huang, Hailong, 2017. "Reducing biogas emissions from village-scale plant with optimal floating-drum biogas storage tank and operation parameters," Applied Energy, Elsevier, vol. 208(C), pages 312-318.
    9. W. Ackooij & S. Demassey & P. Javal & H. Morais & W. Oliveira & B. Swaminathan, 2021. "A bundle method for nonsmooth DC programming with application to chance-constrained problems," Computational Optimization and Applications, Springer, vol. 78(2), pages 451-490, March.
    10. Lukáš Adam & Martin Branda & Holger Heitsch & René Henrion, 2020. "Solving joint chance constrained problems using regularization and Benders’ decomposition," Annals of Operations Research, Springer, vol. 292(2), pages 683-709, September.
    11. Johannes Thürauf, 2022. "Deciding the feasibility of a booking in the European gas market is coNP-hard," Annals of Operations Research, Springer, vol. 318(1), pages 591-618, November.

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