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Robust optimal discrete arc sizing for tree-shaped potential networks

Author

Listed:
  • Martin Robinius

    (Forschungszentrum Jülich GmbH)

  • Lars Schewe

    (Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
    Energie Campus Nürnberg)

  • Martin Schmidt

    (Energie Campus Nürnberg
    Trier University)

  • Detlef Stolten

    (Forschungszentrum Jülich GmbH
    RWTH Aachen University, c/o Institute of Electrochemical Process Engineering (IEK-3), Forschungszentrum Jülich)

  • Johannes Thürauf

    (Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
    Energie Campus Nürnberg)

  • Lara Welder

    (Forschungszentrum Jülich GmbH)

Abstract

We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to be NP-complete even on trees. In order to obtain a tractable problem, we introduce a method for generating a finite scenario set such that optimality of a sizing for this finite set implies the sizing’s optimality for the originally given infinite set of scenarios. We further prove that the size of the finite scenario set is quadratically bounded above in the number of nodes of the underlying tree and that it can be computed in polynomial time. The resulting problem can then be solved as a standard mixed-integer linear optimization problem. Finally, we show the applicability of our theoretical results by computing globally optimal arc sizes for a realistic hydrogen transport network of Eastern Germany.

Suggested Citation

  • Martin Robinius & Lars Schewe & Martin Schmidt & Detlef Stolten & Johannes Thürauf & Lara Welder, 2019. "Robust optimal discrete arc sizing for tree-shaped potential networks," Computational Optimization and Applications, Springer, vol. 73(3), pages 791-819, July.
    • Handle: RePEc:spr:coopap:v:73:y:2019:i:3:d:10.1007_s10589-019-00085-x
    DOI: 10.1007/s10589-019-00085-x
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    References listed on IDEAS

    as
    1. Shiono, Naoshi & Suzuki, Hisatoshi, 2016. "Optimal pipe-sizing problem of tree-shaped gas distribution networks," European Journal of Operational Research, Elsevier, vol. 252(2), pages 550-560.
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    5. Welder, Lara & Ryberg, D.Severin & Kotzur, Leander & Grube, Thomas & Robinius, Martin & Stolten, Detlef, 2018. "Spatio-temporal optimization of a future energy system for power-to-hydrogen applications in Germany," Energy, Elsevier, vol. 158(C), pages 1130-1149.
    6. M. Collins & L. Cooper & R. Helgason & J. Kennington & L. LeBlanc, 1978. "Solving the Pipe Network Analysis Problem Using Optimization Techniques," Management Science, INFORMS, vol. 24(7), pages 747-760, March.
    7. Syranidis, Konstantinos & Robinius, Martin & Stolten, Detlef, 2018. "Control techniques and the modeling of electrical power flow across transmission networks," Renewable and Sustainable Energy Reviews, Elsevier, vol. 82(P3), pages 3452-3467.
    8. Martin Robinius & Alexander Otto & Konstantinos Syranidis & David S. Ryberg & Philipp Heuser & Lara Welder & Thomas Grube & Peter Markewitz & Vanessa Tietze & Detlef Stolten, 2017. "Linking the Power and Transport Sectors—Part 2: Modelling a Sector Coupling Scenario for Germany," Energies, MDPI, vol. 10(7), pages 1-23, July.
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    Cited by:

    1. Lars Schewe & Martin Schmidt & Johannes Thürauf, 2020. "Computing technical capacities in the European entry-exit gas market is NP-hard," Annals of Operations Research, Springer, vol. 295(1), pages 337-362, December.
    2. Lars Schewe & Martin Schmidt & Johannes Thürauf, 2022. "Global optimization for the multilevel European gas market system with nonlinear flow models on trees," Journal of Global Optimization, Springer, vol. 82(3), pages 627-653, March.
    3. Tostado-Véliz, Marcos & Rezaee Jordehi, Ahmad & Mansouri, Seyed Amir & Zhou, Yuekuan & Jurado, Francisco, 2024. "A local electricity-hydrogen market model for industrial parks," Applied Energy, Elsevier, vol. 360(C).
    4. Ralf Lenz & Kai Helge Becker, 2022. "Optimization of capacity expansion in potential-driven networks including multiple looping: a comparison of modelling approaches," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 179-224, March.
    5. Lars Schewe & Martin Schmidt, 2020. "The impact of potential-based physics models on pricing in energy networks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(3), pages 1003-1029, September.
    6. 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.
    7. 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.
    8. Christopher Yeates & Cornelia Schmidt-Hattenberger & Wolfgang Weinzierl & David Bruhn, 2021. "Heuristic Methods for Minimum-Cost Pipeline Network Design – a Node Valency Transfer Metaheuristic," Networks and Spatial Economics, Springer, vol. 21(4), pages 839-871, December.
    9. Reuß, Markus & Grube, Thomas & Robinius, Martin & Stolten, Detlef, 2019. "A hydrogen supply chain with spatial resolution: Comparative analysis of infrastructure technologies in Germany," Applied Energy, Elsevier, vol. 247(C), pages 438-453.
    10. Fränk Plein & Johannes Thürauf & Martine Labbé & Martin Schmidt, 2022. "A bilevel optimization approach to decide the feasibility of bookings in the European gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 409-449, June.

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