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Tight and Compact Sample Average Approximation for Joint Chance-Constrained Problems with Applications to Optimal Power Flow

Author

Listed:
  • Álvaro Porras

    (OASYS Research Group, University of Málaga, 29071 Málaga, Spain)

  • Concepción Domínguez

    (OASYS Research Group, University of Málaga, 29071 Málaga, Spain)

  • Juan Miguel Morales

    (OASYS Research Group, University of Málaga, 29071 Málaga, Spain)

  • Salvador Pineda

    (OASYS Research Group, University of Málaga, 29071 Málaga, Spain)

Abstract

In this paper, we tackle the resolution of chance-constrained problems reformulated via sample average approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program (MIP) cursed with Big-Ms. We introduce an exact resolution method for the MIP that combines the addition of a set of valid inequalities to tighten the linear relaxation bound with coefficient strengthening and constraint screening algorithms to improve its Big-Ms and considerably reduce its size. The proposed valid inequalities are based on the notion of k -envelopes and can be computed off-line using polynomial-time algorithms and added to the MIP program all at once. Furthermore, they are equally useful to boost the strengthening of the Big-Ms and the screening rate of superfluous constraints. We apply our procedures to a probabilistically constrained version of the DC optimal power flow problem with uncertain demand. The chance constraint requires that the probability of violating any of the power system’s constraints be lower than some positive threshold. In a series of numerical experiments that involve five power systems of different size, we show the efficiency of the proposed methodology and compare it with some of the best performing convex inner approximations currently available in the literature.

Suggested Citation

  • Álvaro Porras & Concepción Domínguez & Juan Miguel Morales & Salvador Pineda, 2023. "Tight and Compact Sample Average Approximation for Joint Chance-Constrained Problems with Applications to Optimal Power Flow," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1454-1469, November.
    • Handle: RePEc:inm:orijoc:v:35:y:2023:i:6:p:1454-1469
    DOI: 10.1287/ijoc.2022.0302
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    References listed on IDEAS

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