{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5NFBDIEZWS3VZ23EVEAKD6ETX3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1ee3b7e67ddc8d9926d8af8b8267e4487ac57e3697ba6f153f722d8c37be590b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-07-02T05:29:25Z","title_canon_sha256":"294465d377790d34a35ab0920396fdc6151f7349820f938b02a1a919adf30197"},"schema_version":"1.0","source":{"id":"1507.00431","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00431","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00431v2","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00431","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"5NFBDIEZWS3V","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5NFBDIEZWS3VZ23E","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5NFBDIEZ","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:41cf20b6c4e8da66a8f4b485e3c3675c757d5a751e631360433b1569bc10ea35","target":"graph","created_at":"2026-05-18T00:34:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the problem of voltage stability and reactive power balancing in islanded small-scale electrical networks outfitted with DC/AC inverters (\"microgrids\"). A droop-like voltage feedback controller is proposed which is quadratic in the local voltage magnitude, allowing for the application of circuit-theoretic analysis techniques to the closed-loop system. The operating points of the closed-loop microgrid are in exact correspondence with the solutions of a reduced power flow equation, and we provide explicit solutions and small-signal stability analyses under several static and dynamic ","authors_text":"Florian Dorfler, Francesco Bullo, John W. Simpson-Porco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-07-02T05:29:25Z","title":"Voltage Stabilization in Microgrids via Quadratic Droop Control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00431","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:160c96b1fd1c8ee25ea21e7851c299fc380fd96e2d9b40d73575525fb9bf47bf","target":"record","created_at":"2026-05-18T00:34:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1ee3b7e67ddc8d9926d8af8b8267e4487ac57e3697ba6f153f722d8c37be590b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-07-02T05:29:25Z","title_canon_sha256":"294465d377790d34a35ab0920396fdc6151f7349820f938b02a1a919adf30197"},"schema_version":"1.0","source":{"id":"1507.00431","kind":"arxiv","version":2}},"canonical_sha256":"eb4a11a099b4b75ceb64a900a1f893bee2013c9676ecc43d07b1d70187c3ffc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb4a11a099b4b75ceb64a900a1f893bee2013c9676ecc43d07b1d70187c3ffc8","first_computed_at":"2026-05-18T00:34:45.074324Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:45.074324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M2ueFHeJ3OcFXtZB39xXc+5ITg24jTxo7lrqyQcPEYceWFh704k1j96aZMf/QTYFOdkyPZtoFpr1Bv/CUFmFCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:45.074986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00431","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:160c96b1fd1c8ee25ea21e7851c299fc380fd96e2d9b40d73575525fb9bf47bf","sha256:41cf20b6c4e8da66a8f4b485e3c3675c757d5a751e631360433b1569bc10ea35"],"state_sha256":"19e1dc46789d90806fab8f697d5943c27cbc26189e2c100ced5fbf6c2c9211f4"}