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Mathematical programming formulations for the alternating current optimal power flow problem

Author

Listed:
  • Dan Bienstock

    (Columbia University)

  • Mauro Escobar

    (Institut Polytechnique de Paris)

  • Claudio Gentile

    (IASI, CNR)

  • Leo Liberti

    (Institut Polytechnique de Paris)

Abstract

Power flow refers to the injection of power on the lines of an electrical grid, so that all the injections at the nodes form a consistent flow within the network. Optimality, in this setting, is usually intended as the minimization of the cost of generating power. Current can either be direct or alternating: while the former yields approximate linear programming formulations, the latter yields formulations of a much more interesting sort: namely, nonconvex nonlinear programs in complex numbers. In this technical survey, we derive formulation variants and relaxations of the alternating current optimal power flow problem.

Suggested Citation

  • Dan Bienstock & Mauro Escobar & Claudio Gentile & Leo Liberti, 2020. "Mathematical programming formulations for the alternating current optimal power flow problem," 4OR, Springer, vol. 18(3), pages 249-292, September.
    • Handle: RePEc:spr:aqjoor:v:18:y:2020:i:3:d:10.1007_s10288-020-00455-w
    DOI: 10.1007/s10288-020-00455-w
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    References listed on IDEAS

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    1. Amir Beck & Yuval Beck & Yoash Levron & Alex Shtof & Luba Tetruashvili, 2018. "Globally solving a class of optimal power flow problems in radial networks by tree reduction," Journal of Global Optimization, Springer, vol. 72(3), pages 373-402, November.
    2. Burak Kocuk & Santanu S. Dey & X. Andy Sun, 2016. "Strong SOCP Relaxations for the Optimal Power Flow Problem," Operations Research, INFORMS, vol. 64(6), pages 1177-1196, December.
    3. Ambros M. Gleixner & Timo Berthold & Benjamin Müller & Stefan Weltge, 2017. "Three enhancements for optimization-based bound tightening," Journal of Global Optimization, Springer, vol. 67(4), pages 731-757, April.
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    Cited by:

    1. Sander Claeys & Marta Vanin & Frederik Geth & Geert Deconinck, 2021. "Applications of optimization models for electricity distribution networks," Wiley Interdisciplinary Reviews: Energy and Environment, Wiley Blackwell, vol. 10(5), September.
    2. Yves Crama & Michel Grabisch & Silvano Martello, 2022. "Preface," Annals of Operations Research, Springer, vol. 314(1), pages 1-3, July.
    3. Jens Hönen & Johann L. Hurink & Bert Zwart, 2023. "A classification scheme for local energy trading," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 85-118, March.
    4. Yves Crama & Michel Grabisch & Silvano Martello, 2021. "4OR comes of age," 4OR, Springer, vol. 19(1), pages 1-13, March.
    5. Jie Wang & Victor Magron, 2022. "Exploiting Sparsity in Complex Polynomial Optimization," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 335-359, January.
    6. Daniel Bienstock & Mauro Escobar & Claudio Gentile & Leo Liberti, 2022. "Mathematical programming formulations for the alternating current optimal power flow problem," Annals of Operations Research, Springer, vol. 314(1), pages 277-315, July.
    7. Kevin-Martin Aigner & Robert Burlacu & Frauke Liers & Alexander Martin, 2023. "Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 458-474, March.
    8. Bichler, Martin & Knörr, Johannes, 2023. "Getting prices right on electricity spot markets: On the economic impact of advanced power flow models," Energy Economics, Elsevier, vol. 126(C).

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