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A joint model of probabilistic/robust constraints for gas transport management in stationary networks

Author

Listed:
  • T. González Grandón

    (Humboldt University Berlin)

  • H. Heitsch

    (Weierstrass Institute for Applied Analysis and Stochastics)

  • R. Henrion

    (Weierstrass Institute for Applied Analysis and Stochastics)

Abstract

We present a novel mathematical algorithm to assist gas network operators in managing uncertainty, while increasing reliability of transmission and supply. As a result, we solve an optimization problem with a joint probabilistic constraint over an infinite system of random inequalities. Such models arise in the presence of uncertain parameters having partially stochastic and partially non-stochastic character. The application that drives this new approach is a stationary network with uncertain demand (which are stochastic due to the possibility of fitting statistical distributions based on historical measurements) and with uncertain roughness coefficients in the pipes (which are uncertain but non-stochastic due to a lack of attainable measurements). We study the sensitivity of local uncertainties in the roughness coefficients and their impact on a highly reliable network operation. In particular, we are going to answer the question, what is the maximum uncertainty that is allowed (shaping a ’maximal’ uncertainty set) around nominal roughness coefficients, such that random demands in a stationary gas network can be satisfied at given high probability level for no matter which realization of true roughness coefficients within the uncertainty set. One ends up with a constraint, which is probabilistic with respect to the load of gas and robust with respect to the roughness coefficients. We demonstrate how such constraints can be dealt with in the framework of the so-called spheric-radial decomposition of multivariate Gaussian distributions. The numerical solution of a corresponding optimization problem is illustrated. The results might assist the network operator with the implementation of cost-intensive roughness measurements.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:comgts:v:14:y:2017:i:3:d:10.1007_s10287-017-0284-7
    DOI: 10.1007/s10287-017-0284-7
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    References listed on IDEAS

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    1. W. Ackooij & A. Frangioni & W. Oliveira, 2016. "Inexact stabilized Benders’ decomposition approaches with application to chance-constrained problems with finite support," Computational Optimization and Applications, Springer, vol. 65(3), pages 637-669, December.
    2. 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.
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    Citations

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    Cited by:

    1. Holger Berthold & Holger Heitsch & René Henrion & Jan Schwientek, 2022. "On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 1-37, August.
    2. Farrokhifar, Meisam & Nie, Yinghui & Pozo, David, 2020. "Energy systems planning: A survey on models for integrated power and natural gas networks coordination," Applied Energy, Elsevier, vol. 262(C).
    3. 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.
    4. 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.
    5. 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.

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