{"paper":{"title":"Synchronization of cyclic power grids: equilibria and stability of the synchronous state","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"nlin.CD","authors_text":"Haixiang Lin, Johan.L.A. Dubbeldam, Kaihua Xi","submitted_at":"2016-10-03T14:52:30Z","abstract_excerpt":"Synchronization is essential for proper functioning of the power grid. We investigate the synchronous state and its stability for a network with a cyclic topology and with the evolution of the states satisfying the swing equations. We calculate the number of stable equilibria and investigate both the linear and nonlinear stability of the synchronous state. The linear stability analysis shows that the stability of the state, determined by the smallest nonzero eigenvalue, is inversely proportional to the size of the network. The nonlinear stability, which we calculated by comparing the potential"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01003","kind":"arxiv","version":1},"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"}