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Mathematical Properties of Formulations of the Gas Transmission Problem

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  • Daniel de Wolf

    (TVES - Territoires, Villes, Environnement & Société - ULR 4477 - ULCO - Université du Littoral Côte d'Opale - Université de Lille, ULCO - Université du Littoral Côte d'Opale)

Abstract

The paper presents the mathematical properties of several formulations for the gas transmission problem that account for the nonlinear flow pressure relations. The form of the nonlinear flow pressure relations is such that the model is in general nonconvex. However, we show here that under a restrictive condition (gas inlet or gas pressure fixed at every entry/outgoing node) the problem becomes convex. This result is obtained by use of the variational inequality theory. We also give a computational method to find a feasible solution to the problem and give a physical interpretation to this feasible solution.

Suggested Citation

  • Daniel de Wolf, 2017. "Mathematical Properties of Formulations of the Gas Transmission Problem," Post-Print halshs-02396747, HAL.
    • Handle: RePEc:hal:journl:halshs-02396747
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-02396747
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    References listed on IDEAS

    as
    1. Roger Ríos-Mercado & Suming Wu & L. Scott & E. Boyd, 2002. "A Reduction Technique for Natural Gas Transmission Network Optimization Problems," Annals of Operations Research, Springer, vol. 117(1), pages 217-234, November.
    2. DE WOLF, Daniel & SMEERS, Yves, 2000. "The gas transmission problem solved by an extension of the simplex algorithm," LIDAM Reprints CORE 1489, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. De Wolf, D. & Smeers, Y., 1996. "Optimal dimensioning of pipe networks with application to gas transmission networks," LIDAM Reprints CORE 1249, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Daniel de Wolf & Yves Smeers, 1996. "Optimal Dimensioning of Pipe Networks with Application to Gas Transmission Networks," Operations Research, INFORMS, vol. 44(4), pages 596-608, August.
    5. André, Jean & Auray, Stéphane & Brac, Jean & De Wolf, Daniel & Maisonnier, Guy & Ould-Sidi, Mohamed-Mahmoud & Simonnet, Antoine, 2013. "Design and dimensioning of hydrogen transmission pipeline networks," European Journal of Operational Research, Elsevier, vol. 229(1), pages 239-251.
    6. Richard P. O'Neill & Mark Williard & Bert Wilkins & Ralph Pike, 1979. "A Mathematical Programming Model for Allocation of Natural Gas," Operations Research, INFORMS, vol. 27(5), pages 857-873, October.
    7. Jean André & Stéphane Auray & Daniel de Wolf & Mohamed-Mahmoud Memmah & Antoine Simonnet, 2014. "Time development of new hydrogen transmission pipeline networks for France," Post-Print halshs-02396799, HAL.
    8. Ríos-Mercado, Roger Z. & Borraz-Sánchez, Conrado, 2015. "Optimization problems in natural gas transportation systems: A state-of-the-art review," Applied Energy, Elsevier, vol. 147(C), pages 536-555.
    9. Daniel De Wolf & Yves Smeers, 2000. "The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm," Management Science, INFORMS, vol. 46(11), pages 1454-1465, November.
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    Cited by:

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