Polynomial SDP cuts for Optimal Power Flow

Hassan Hijazi, Carleton Coffrin, Pascal Van Hentenryck

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    25 Citations (Scopus)

    Abstract

    The use of convex relaxations has lately gained considerable interest in Power Systems. These relaxations play a major role in providing quality guarantees for non-convex optimization problems. For the Optimal Power Flow (OPF) problem, the semidefinite programming (SDP) relaxation is known to produce tight lower bounds. Unfortunately, SDP solvers still suffer from a lack of scalability. In this work, we introduce an exact reformulation of the SDP relaxation, formed by a set of polynomial constraints defined in the space of real variables. The new constraints can be seen as "cuts", strengthening weaker second-order cone relaxations, and can be generated in a lazy iterative fashion. The new formulation can be handled by standard nonlinear programming solvers, enjoying better stability and computational efficiency. This new approach benefits from recent results on tree-decomposition methods, reducing the dimension of the underlying SDP matrices. As a side result, we present a formulation of Kirchhoff's Voltage Law in the SDP space and reveal the existing link between these cycle constraints and the original SDP relaxation for three dimensional matrices. Preliminary results show a significant gain in computational efficiency compared to a standard SDP solver approach.

    Original languageEnglish
    Title of host publication19th Power Systems Computation Conference, PSCC 2016
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    ISBN (Electronic)9788894105124
    DOIs
    Publication statusPublished - 10 Aug 2016
    Event19th Power Systems Computation Conference, PSCC 2016 - Genova, Italy
    Duration: 20 Jun 201624 Jun 2016

    Publication series

    Name19th Power Systems Computation Conference, PSCC 2016

    Conference

    Conference19th Power Systems Computation Conference, PSCC 2016
    Country/TerritoryItaly
    CityGenova
    Period20/06/1624/06/16

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