{
  "abstract": "Levenberg-Marquardt power flow (LMPF) addresses ill-conditioned equations and provides least-squares stationary points for infeasible operating requests. Conventional implementations form damped normal equations, where J^T J introduces fill, squares the spectral condition number of the undamped part, and adds sparse-product cost. We propose an augmented LMPF formulation with a symbolic-permutation-based Jacobian operator that fills the augmented blocks directly. We prove that the matrix is symmetric quasi-definite for positive damping, enabling fixed-order, pivot-free QDLDL factorization. This property also motivates the solver choice: KLU value-only refactorization can reuse an unsuitable pivot order, forcing fresh full factorizations on difficult LMPF trajectories. We further introduce one-probe adaptive trust-region initialization for the radius and damping. Direct assembly is 7.5-11.9x faster than the fastest coordinate-list path and 18.0-58.8x faster than cached normal-equation sparse-product formation; QDLDL reduces numerical refactorization and triangular-solve time by up to 3.40x on identical matrices. Adaptive initialization solves flat-started RTE cases in 19-25 factorizations, 7.5-11.6x faster than reproduced three-step LM. On case2383wp, our 84-iteration run performs 84 factorizations and 168 resolves in 237 ms, versus published times of 200.780-441.72 s with fewer outer iterations, corresponding to speedups of 847-1860x. These results require complete factorization and resolve accounting and reveal initialization and legacy-parameter effects. DC-initialized NR exhibits fast quadratic convergence throughout every tested solvable loading range, motivating clearer, reproducible definitions of ill-conditioned power-flow benchmarks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34509",
  "author_total": 2,
  "authors": [
    {
      "name": "Tianshi Cheng"
    },
    {
      "name": "Venkata Dinavahi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8fm02acsk098s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34509",
  "fulltext_url": null,
  "id": "8fm02acsk098s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34509",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "cs.PF"
    ],
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2208|Optimal Power Flow Distribution"
    ]
  ],
  "openalex": "W7223885995",
  "pdf_url": "https://arxiv.org/pdf/2610.34509",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8fm02acsk098s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34509",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34509"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Symbolic Direct Construction of Augmented Systems for Levenberg-Marquardt Power Flow",
  "title_text": "Symbolic Direct Construction of Augmented Systems for Levenberg-Marquardt Power Flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/8fm02acsk098s",
  "venue": "arXiv",
  "versions": []
}