{
  "id": "2505.06211",
  "version": "v1",
  "published": "2025-05-09T17:41:40.000Z",
  "updated": "2025-05-09T17:41:40.000Z",
  "title": "Alternating Methods for Large-Scale AC Optimal Power Flow with Unit Commitment",
  "authors": [
    "Matthew Brun",
    "Thomas Lee",
    "Dirk Lauinger",
    "Xin Chen",
    "Xu Andy Sun"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "Security-constrained unit commitment with alternating current optimal power flow (SCUC-ACOPF) is a central problem in power grid operations that optimizes commitment and dispatch of generators under a physically accurate power transmission model while encouraging robustness against component failures. SCUC-ACOPF requires solving large-scale problems that involve multiple time periods and networks with thousands of buses within strict time limits. In this work, we study a detailed SCUC-ACOPF model with a rich set of features of modern power grids, including price-sensitive load, reserve products, transformer controls, and energy-limited devices. We propose a decomposition scheme and a penalty alternating direction method to find high-quality solutions to this model. Our methodology leverages spatial and temporal decomposition, separating the problem into a set of mixed-integer linear programs for each bus and a set of continuous nonlinear programs for each time period. To improve the performance of the algorithm, we introduce a variety of heuristics, including restrictions of temporal linking constraints, a second-order cone relaxation, and a contingency screening algorithm. We quantify the quality of feasible solutions through a dual bound from a convex second-order cone program. To evaluate our algorithm, we use large-scale test cases from Challenge 3 of the U.S. Department of Energy's Grid Optimization Competition that resemble real power grid data under a variety of operating conditions and decision horizons. The experiments yield feasible solutions with an average optimality gap of 1.33%, demonstrating that this approach generates near-optimal solutions within stringent time limits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-09T17:41:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49M27",
      "90C06",
      "90B99"
    ],
    "keywords": [
      "large-scale ac optimal power flow",
      "unit commitment",
      "accurate power transmission model",
      "current optimal power flow",
      "real power grid data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}