{"id":"https://openalex.org/W3091250964","doi":"https://doi.org/10.1109/tcns.2020.3027783","title":"Uniqueness of Power Flow Solutions Using Monotonicity and Network Topology","display_name":"Uniqueness of Power Flow Solutions Using Monotonicity and Network Topology","publication_year":2020,"publication_date":"2020-09-29","ids":{"openalex":"https://openalex.org/W3091250964","doi":"https://doi.org/10.1109/tcns.2020.3027783","mag":"3091250964"},"language":"en","primary_location":{"id":"doi:10.1109/tcns.2020.3027783","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2020.3027783","pdf_url":null,"source":{"id":"https://openalex.org/S2502544478","display_name":"IEEE Transactions on Control of Network Systems","issn_l":"2325-5870","issn":["2325-5870","2372-2533"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Control of Network Systems","raw_type":"journal-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/A5033146280","display_name":"SangWoo Park","orcid":"https://orcid.org/0000-0002-0355-7272"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"SangWoo Park","raw_affiliation_strings":["Department of Industrial Engineering and Operations Research, University of California Berkeley, Berkeley, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research, University of California Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079119611","display_name":"Richard Y. Zhang","orcid":"https://orcid.org/0000-0003-3980-2791"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard Y. Zhang","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Champaign, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Champaign, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042580848","display_name":"Javad Lavaei","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Javad Lavaei","raw_affiliation_strings":["Department of Industrial Engineering and Operations Research, University of California Berkeley, Berkeley, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research, University of California Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091425870","display_name":"Ross Baldick","orcid":"https://orcid.org/0000-0003-2783-7321"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ross Baldick","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, TX, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5033146280"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":0.6165,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.68121152,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"8","issue":"1","first_page":"319","last_page":"330"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10454","display_name":"Optimal Power Flow Distribution","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10305","display_name":"Power System Optimization and Stability","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11941","display_name":"Power System Reliability and Maintenance","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.696122944355011},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.6944657564163208},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6493158936500549},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.631608247756958},{"id":"https://openalex.org/keywords/power-flow","display_name":"Power flow","score":0.5400157570838928},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5378275513648987},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4997539520263672},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.41794759035110474},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.37800201773643494},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.377561092376709},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37042421102523804},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.32916533946990967},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2656824290752411},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.13980326056480408},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.130097895860672},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12081596255302429},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08460178971290588}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.696122944355011},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6944657564163208},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6493158936500549},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.631608247756958},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.5400157570838928},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5378275513648987},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4997539520263672},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.41794759035110474},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.37800201773643494},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.377561092376709},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37042421102523804},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.32916533946990967},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2656824290752411},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.13980326056480408},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.130097895860672},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12081596255302429},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08460178971290588},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcns.2020.3027783","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2020.3027783","pdf_url":null,"source":{"id":"https://openalex.org/S2502544478","display_name":"IEEE Transactions on Control of Network Systems","issn_l":"2325-5870","issn":["2325-5870","2372-2533"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Control of Network Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5600000023841858,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1847539667","https://openalex.org/W1984452440","https://openalex.org/W1997635994","https://openalex.org/W2014035031","https://openalex.org/W2038372718","https://openalex.org/W2039558417","https://openalex.org/W2051790896","https://openalex.org/W2062451421","https://openalex.org/W2076963109","https://openalex.org/W2092909860","https://openalex.org/W2106424475","https://openalex.org/W2111198155","https://openalex.org/W2117549465","https://openalex.org/W2138378881","https://openalex.org/W2147665001","https://openalex.org/W2202972443","https://openalex.org/W2578606504","https://openalex.org/W2614006387","https://openalex.org/W2932078621","https://openalex.org/W2939282870","https://openalex.org/W2949368647","https://openalex.org/W2962963296","https://openalex.org/W2963059498","https://openalex.org/W2963422512","https://openalex.org/W2964100695","https://openalex.org/W2990566680","https://openalex.org/W3091250964","https://openalex.org/W3106224369","https://openalex.org/W4288366216","https://openalex.org/W4288615150","https://openalex.org/W6665950833","https://openalex.org/W6761964457","https://openalex.org/W6784035364","https://openalex.org/W6841128325"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W2963662567","https://openalex.org/W4321473471"],"abstract_inverted_index":{"This":[0],"article":[1],"establishes":[2],"sufficient":[3],"conditions":[4,129],"for":[5,41,49,119,164],"the":[6,14,22,31,63,69,78,82,111,120,128,132,141,165,170],"uniqueness":[7,171],"of":[8,81,89,106,116,172],"AC":[9],"power":[10,19,33,52,108,122,166,173],"flow":[11,20,34,123,174],"solutions":[12,59],"via":[13],"monotonic":[15],"relationship":[16],"between":[17],"real":[18,107],"and":[21,153,161],"phase":[23,91,101],"angle":[24,66],"difference.":[25],"More":[26],"specifically,":[27],"we":[28,54],"prove":[29],"that":[30,56,65,126,155],"P-\u0398":[32],"problem":[35,133],"has":[36,134],"at":[37],"most":[38],"one":[39],"solution":[40,139],"any":[42],"acyclic":[43],"or":[44],"GSP":[45],"graph.":[46],"In":[47,84],"addition,":[48],"arbitrary":[50],"cyclic":[51],"networks,":[53],"show":[55,154],"multiple":[57],"distinct":[58],"cannot":[60],"exist":[61],"under":[62,127],"assumption":[64],"differences":[67],"across":[68],"lines":[70],"are":[71,145],"bounded":[72],"by":[73],"some":[74],"limit":[75],"related":[76],"to":[77,98],"maximal":[79],"girth":[80],"network.":[83],"these":[85],"cases,":[86],"a":[87,104,135,150,159],"vector":[88,105],"voltage":[90,143],"angles":[92],"can":[93],"be":[94],"uniquely":[95],"determined":[96],"(up":[97],"an":[99],"absolute":[100],"shift)":[102],"given":[103],"injections":[109],"within":[110],"realizable":[112,138],"range.":[113],"The":[114],"implication":[115],"this":[117,156],"result":[118],"classical":[121],"analysis":[124],"is":[125],"specified":[130],"above,":[131],"unique":[136],"physically":[137],"if":[140],"phasor":[142],"magnitudes":[144],"fixed.":[146],"We":[147],"also":[148],"introduce":[149],"series-parallel":[151],"operator":[152,157],"obtains":[158],"reduced":[160],"easier-to-analyze":[162],"model":[163],"system":[167],"without":[168],"changing":[169],"solutions.":[175]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
