{
  "id": "2104.03107",
  "version": "v1",
  "published": "2021-04-07T13:13:07.000Z",
  "updated": "2021-04-07T13:13:07.000Z",
  "title": "Adjustable Robust Two-Stage Polynomial Optimization with Application to AC Optimal Power Flow",
  "authors": [
    "Olga Kuryatnikova",
    "Bissan Ghaddar",
    "Daniel K. Molzahn"
  ],
  "comment": "28 pages, 3 tables",
  "categories": [
    "math.OC"
  ],
  "abstract": "In this work, we consider two-stage polynomial optimization problems under uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the uncertainty is revealed and the rest of optimization variables (state variables) are set up as a solution to a known system of possibly non-linear equations. This type of problem occurs, for instance, in optimization for dynamical systems, such as electric power systems. We combine tools from polynomial and robust optimization to provide a framework for general adjustable robust polynomial optimization problems. In particular, we propose an iterative algorithm to build a sequence of (approximately) robustly feasible solutions with an improving objective value and verify robust feasibility or infeasibility of the resulting solution under a semialgebraic uncertainty set. At each iteration, the algorithm optimizes over a subset of the feasible set and uses affine approximations of the second-stage equations while preserving the non-linearity of other constraints. The algorithm allows for additional simplifications in case of possibly non-convex quadratic problems under ellipsoidal uncertainty. We implement our approach for AC Optimal Power Flow and demonstrate the performance of our proposed method on Matpower instances.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-07T13:13:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ac optimal power flow",
      "adjustable robust two-stage polynomial optimization",
      "robust polynomial optimization",
      "polynomial optimization problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}