{"paper":{"title":"Spectral solution of load flow equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"physics.class-ph","authors_text":"A. Knippel, J. G. Caputo, N. Retiere","submitted_at":"2018-08-14T18:25:21Z","abstract_excerpt":"The load-flow equations are the main tool to operate and plan electrical networks. For transmission or distribution networks these equations can be simplified into a linear system involving the graph Laplacian and the power input vector. We show, using spectral graph theory, how to solve this system efficiently. This spectral approach gives a new geometric view of the network and power vector. This formulation yields a Parseval-like relation for the $L_2$ norm of the power in the lines. Using this relation as a guide, we show that a small number of eigenvector components of the power vector ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06906","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}