{
  "id": "2211.03969",
  "version": "v1",
  "published": "2022-11-08T02:56:47.000Z",
  "updated": "2022-11-08T02:56:47.000Z",
  "title": "Pitfalls of Zero Voltage Values in Optimal Power Flow Problems",
  "authors": [
    "Frederik Geth"
  ],
  "comment": "5 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "The existence of strictly positive lower bounds on voltage magnitude is taken for granted in optimal power flow problems. Nevertheless, it not possible to rely on such bounds for a variety of real-world network optimization problems. This paper discusses a few issues related to 0\\,V assumptions made during the process of deriving optimization formulations in a the current-voltage, power-voltage and power-lifted-voltage variable spaces. The differences between the assumptions are illustrated for a 2-bus 2-wire test case, where the feasible sets are visualized. A nonzero relaxation gap is observed for the canonical multiconductor nonlinear power-voltage formulation. A zero gap can be obtained for the branch flow model semi-definite relaxation, using newly proposed valid equalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-08T02:56:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal power flow problems",
      "zero voltage values",
      "multiconductor nonlinear power-voltage formulation",
      "branch flow model semi-definite relaxation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}