{"paper":{"title":"Calculating Domain of Attraction Boundary of Power Systems Based on the Gentlest Ascent Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The domain of attraction boundary in power systems equals the closure of the union of stable manifolds of index-1 critical elements.","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.DS","authors_text":"Aiqing Zhu, Chenmin Zhang, Jianxi Lin, Sixu Wu, Yang Liu, Yifa Tang","submitted_at":"2026-05-05T18:40:38Z","abstract_excerpt":"The power system, a fundamental public utility, is increasingly important due to growing global electricity demand. Recent large-scale blackouts (e.g., Iberian Peninsula, UK) have raised concerns about transient stability under impact faults. Transient stability is determined by post-disturbance synchronizing capability of synchronous generators, formulated as identifying the domain of attraction (DOA) boundary of the asymptotically stable equilibrium. Using a benchmark model of synchronous-generator-dominated power systems, this report employs a gentlest ascent dynamics (GAD) method for 1-sad"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Theoretically, under certain assumptions we prove that the DOA boundary is the closure of the union of stable manifolds of index-1 critical elements, and establish a stability theory for a perturbed GAD system.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The unspecified 'certain assumptions' required for the proof that the DOA boundary equals the closure of the union of stable manifolds of index-1 critical elements; these assumptions are invoked in the theoretical results but not detailed in the abstract.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The domain of attraction boundary for stable power system equilibria is the closure of the union of stable manifolds of index-1 critical elements, computed via gentlest ascent dynamics, adjoint methods for periodic orbits, and stable manifold algorithms.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The domain of attraction boundary in power systems equals the closure of the union of stable manifolds of index-1 critical elements.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"74fbb7ad44455b0dfba995186c874a2f593ad7e72748fff7cd0524f497bd073f"},"source":{"id":"2605.04197","kind":"arxiv","version":2},"verdict":{"id":"d62669b6-693c-40b2-8ae1-1e31a656aa26","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T17:44:14.023594Z","strongest_claim":"Theoretically, under certain assumptions we prove that the DOA boundary is the closure of the union of stable manifolds of index-1 critical elements, and establish a stability theory for a perturbed GAD system.","one_line_summary":"The domain of attraction boundary for stable power system equilibria is the closure of the union of stable manifolds of index-1 critical elements, computed via gentlest ascent dynamics, adjoint methods for periodic orbits, and stable manifold algorithms.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The unspecified 'certain assumptions' required for the proof that the DOA boundary equals the closure of the union of stable manifolds of index-1 critical elements; these assumptions are invoked in the theoretical results but not detailed in the abstract.","pith_extraction_headline":"The domain of attraction boundary in power systems equals the closure of the union of stable manifolds of index-1 critical elements."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.04197/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:21.164819Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T14:42:22.945293Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"915b44f203ed6f47d65a6bb6d1dc95365de8842815c86ebe86fc0716d8d9f7bd"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":3,"snapshot_sha256":"56ec7dfde070a5bbe33690fba8f4610d331d5dd9826f3d763236c97c19b311fa"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}