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Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

Author

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  • Ksenia Bestuzheva

    (Data61-CSIRO, Australian National University, Canberra 2601, Australia; Zuse Institute Berlin, 14195 Berlin, Germany)

  • Hassan Hijazi

    (Los Alamos National Laboratory, Los Alamos, New Mexico 87545)

  • Carleton Coffrin

    (Los Alamos National Laboratory, Los Alamos, New Mexico 87545)

Abstract

This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the optimal transmission switching problem in power systems. Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. The tightened model has promising computational results when compared with state-of-the-art formulations.

Suggested Citation

  • Ksenia Bestuzheva & Hassan Hijazi & Carleton Coffrin, 2020. "Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 682-696, July.
    • Handle: RePEc:inm:orijoc:v:32:y:3:i:2020:p:682-696
    DOI: 10.1287/ijoc.2019.0900
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    References listed on IDEAS

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    1. Ghaddar, Bissan & Jabr, Rabih A., 2019. "Power transmission network expansion planning: A semidefinite programming branch-and-bound approach," European Journal of Operational Research, Elsevier, vol. 274(3), pages 837-844.
    2. Pietro Belotti & Pierre Bonami & Matteo Fischetti & Andrea Lodi & Michele Monaci & Amaya Nogales-Gómez & Domenico Salvagnin, 2016. "On handling indicator constraints in mixed integer programming," Computational Optimization and Applications, Springer, vol. 65(3), pages 545-566, December.
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    Cited by:

    1. Jay, Devika & Swarup, K.S., 2021. "A comprehensive survey on reactive power ancillary service markets," Renewable and Sustainable Energy Reviews, Elsevier, vol. 144(C).

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