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Mathematical programming formulations for the alternating current optimal power flow problem

Author

Listed:
  • Daniel Bienstock

    (Columbia University)

  • Mauro Escobar

    (Institut Polytechnique de Paris)

  • Claudio Gentile

    (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

  • 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.
    • Handle: RePEc:spr:annopr:v:314:y:2022:i:1:d:10.1007_s10479-021-04497-z
    DOI: 10.1007/s10479-021-04497-z
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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. 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.

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