{"id":"https://openalex.org/W2496118591","doi":"https://doi.org/10.1109/acc.2016.7525174","title":"Monotone operator approach to power flow solutions","display_name":"Monotone operator approach to power flow solutions","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2496118591","doi":"https://doi.org/10.1109/acc.2016.7525174","mag":"2496118591"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2016.7525174","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2016.7525174","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 American Control Conference (ACC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050954769","display_name":"Krishnamurthy Dvijotham","orcid":"https://orcid.org/0000-0002-1328-4677"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Krishnamurthy Dvijotham","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068974029","display_name":"Michael Chertkov","orcid":"https://orcid.org/0000-0002-6758-515X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Chertkov","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5069455858","display_name":"Steven H. Low","orcid":"https://orcid.org/0000-0001-6476-3048"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steven Low","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050954769"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.312,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.61511349,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1769","last_page":"1769"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6980109214782715},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.649497389793396},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.635967493057251},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6297832727432251},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5835500955581665},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5577904582023621},{"id":"https://openalex.org/keywords/power-flow","display_name":"Power flow","score":0.5296525359153748},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.5146895051002502},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5065315961837769},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4642079472541809},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4440794885158539},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.4288121461868286},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.4272310137748718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41673707962036133},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3462209105491638},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16751199960708618},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07144513726234436},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06170818209648132}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6980109214782715},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.649497389793396},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.635967493057251},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6297832727432251},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5835500955581665},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5577904582023621},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.5296525359153748},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.5146895051002502},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5065315961837769},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4642079472541809},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4440794885158539},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.4288121461868286},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.4272310137748718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41673707962036133},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3462209105491638},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16751199960708618},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07144513726234436},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06170818209648132},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/acc.2016.7525174","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2016.7525174","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 American Control Conference (ACC)","raw_type":"proceedings-article"},{"id":"pmh:oai:authors.library.caltech.edu:80107","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20170810-111302484","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4301895170","https://openalex.org/W2963936214","https://openalex.org/W2610026222","https://openalex.org/W2784024314","https://openalex.org/W1970485118","https://openalex.org/W4249252985","https://openalex.org/W3093949365","https://openalex.org/W1481475550","https://openalex.org/W2085901578","https://openalex.org/W3122495059"],"abstract_inverted_index":{"Summary":[0],"form":[1],"only":[2],"given.":[3],"The":[4,50],"AC":[5],"power":[6,14,43,63],"flow":[7,44,64],"equations":[8],"underlie":[9],"all":[10],"operational":[11],"aspects":[12],"of":[13,27,52],"systems.":[15],"In":[16],"this":[17,22,75],"paper,":[18],"Here":[19],"we":[20],"solve":[21],"problem":[23],"using":[24],"the":[25,42,57,62,90,102],"theory":[26],"monotone":[28],"operators.":[29],"We":[30,100],"show":[31],"that":[32,67,83,94],"it":[33],"is":[34,78],"possible":[35],"to":[36,71],"characterize":[37],"a":[38,79,87],"\u201ccontractivity":[39],"domain\u201d":[40],"in":[41,89,98],"variables":[45],"(voltage":[46],"magnitudes":[47],"and":[48],"phases).":[49],"construction":[51],"these":[53],"domains":[54],"depends":[55],"on":[56,104],"specific":[58],"representation":[59],"chosen":[60],"for":[61],"equations,":[65],"so":[66],"different":[68,72],"representations":[69],"lead":[70],"domains.":[73],"Given":[74],"domain,":[76,91],"there":[77],"simple":[80],"efficient":[81],"algorithm":[82],"will":[84],"either":[85],"find":[86],"solution":[88],"or":[92],"certify":[93],"no":[95],"solutions":[96],"exist":[97],"it.":[99],"validate":[101],"approach":[103],"several":[105],"IEEE":[106],"test":[107],"cases.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
