{
  "id": "1404.5071",
  "version": "v2",
  "published": "2014-04-20T21:11:08.000Z",
  "updated": "2014-11-17T17:57:17.000Z",
  "title": "Sparsity-Exploiting Moment-Based Relaxations of the Optimal Power Flow Problem",
  "authors": [
    "Daniel K. Molzahn",
    "Ian A. Hiskens"
  ],
  "comment": "14 pages, 3 figures. To appear in IEEE Transactions on Power Systems. arXiv admin note: text overlap with arXiv:1312.1992",
  "categories": [
    "math.OC"
  ],
  "abstract": "Convex relaxations of non-convex optimal power flow (OPF) problems have recently attracted significant interest. While existing relaxations globally solve many OPF problems, there are practical problems for which existing relaxations fail to yield physically meaningful solutions. This paper applies moment relaxations to solve many of these OPF problems. The moment relaxations are developed from the Lasserre hierarchy for solving generalized moment problems. Increasing the relaxation order in this hierarchy results in \"tighter\" relaxations at the computational cost of larger semidefinite programs. Low-order moment relaxations are capable of globally solving many small OPF problems for which existing relaxations fail. By exploiting sparsity and only applying the higher-order relaxation to specific buses, global solutions to larger problems are computationally tractable through the use of an iterative algorithm informed by a heuristic for choosing where to apply the higher-order constraints. With standard semidefinite programming solvers, the algorithm globally solves many test systems with up to 300 buses for which the existing semidefinite relaxation fails to yield globally optimal solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-20T21:11:08.000Z",
      "abstract": "Convex relaxations of non-convex optimal power flow (OPF) problems have recently attracted significant interest. While existing relaxations globally solve many OPF problems, there are practical problems for which existing relaxations fail to yield physically meaningful solutions. This paper applies moment-based convex relaxations to solve many of these OPF problems. The moment-based relaxations are developed from the Lasserre hierarchy for solving generalized moment problems. Increasing the relaxation order in this hierarchy results in \"tighter\" relaxations at the computational cost of larger semidefinite programs. Low-order moment-based relaxations are capable of solving many small OPF problems for which existing relaxations fail. By exploiting sparsity and only applying the higher-order relaxation to specific buses, global solutions to larger problems are computationally tractable through the use of an iterative algorithm informed by a heuristic for choosing where to apply the higher-order constraints. Global solution of several test systems, including the IEEE 300-bus system, prove the effectiveness of this algorithm.",
      "comment": "10 pages, 1 figure. arXiv admin note: text overlap with arXiv:1312.1992",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-17T17:57:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal power flow problem",
      "sparsity-exploiting moment-based relaxations",
      "opf problems",
      "existing relaxations fail",
      "paper applies moment-based convex relaxations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.5071M"
    }
  }
}