{"id":"https://openalex.org/W4315629712","doi":"https://doi.org/10.1109/globecom48099.2022.10000707","title":"Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Duality","display_name":"Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Duality","publication_year":2022,"publication_date":"2022-12-04","ids":{"openalex":"https://openalex.org/W4315629712","doi":"https://doi.org/10.1109/globecom48099.2022.10000707"},"language":"en","primary_location":{"id":"doi:10.1109/globecom48099.2022.10000707","is_oa":false,"landing_page_url":"https://doi.org/10.1109/globecom48099.2022.10000707","pdf_url":null,"source":{"id":"https://openalex.org/S4363607705","display_name":"GLOBECOM 2022 - 2022 IEEE Global Communications Conference","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"GLOBECOM 2022 - 2022 IEEE Global Communications Conference","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/A5101985062","display_name":"Kejun Chen","orcid":"https://orcid.org/0000-0002-2162-7887"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kejun Chen","raw_affiliation_strings":["University of California,Department of Electrical and Computer Engineering,Santa Cruz","Department of Electrical and Computer Engineering, University of California, Santa Cruz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California,Department of Electrical and Computer Engineering,Santa Cruz","institution_ids":["https://openalex.org/I185103710"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Santa Cruz","institution_ids":["https://openalex.org/I185103710"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029168975","display_name":"Shourya Bose","orcid":"https://orcid.org/0000-0002-2081-9545"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shourya Bose","raw_affiliation_strings":["University of California,Department of Electrical and Computer Engineering,Santa Cruz","Department of Electrical and Computer Engineering, University of California, Santa Cruz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California,Department of Electrical and Computer Engineering,Santa Cruz","institution_ids":["https://openalex.org/I185103710"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Santa Cruz","institution_ids":["https://openalex.org/I185103710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100433414","display_name":"Yu Zhang","orcid":"https://orcid.org/0000-0001-7889-2676"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yu Zhang","raw_affiliation_strings":["University of California,Department of Electrical and Computer Engineering,Santa Cruz","Department of Electrical and Computer Engineering, University of California, Santa Cruz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California,Department of Electrical and Computer Engineering,Santa Cruz","institution_ids":["https://openalex.org/I185103710"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Santa Cruz","institution_ids":["https://openalex.org/I185103710"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I185103710"],"apc_list":null,"apc_paid":null,"fwci":3.1892,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.94323116,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"5305","last_page":"5310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9997000098228455,"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":0.9988999962806702,"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/computer-science","display_name":"Computer science","score":0.6416944861412048},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6278594136238098},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5780892968177795},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.517020583152771},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5088677406311035},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.4822900593280792},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.42470836639404297},{"id":"https://openalex.org/keywords/offline-learning","display_name":"Offline learning","score":0.41701436042785645},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3483872413635254},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25128671526908875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1844043731689453}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6416944861412048},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6278594136238098},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5780892968177795},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.517020583152771},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5088677406311035},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.4822900593280792},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.42470836639404297},{"id":"https://openalex.org/C2780490138","wikidata":"https://www.wikidata.org/wiki/Q7079636","display_name":"Offline learning","level":3,"score":0.41701436042785645},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3483872413635254},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25128671526908875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1844043731689453},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C2986087404","wikidata":"https://www.wikidata.org/wiki/Q15946010","display_name":"Online learning","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/globecom48099.2022.10000707","is_oa":false,"landing_page_url":"https://doi.org/10.1109/globecom48099.2022.10000707","pdf_url":null,"source":{"id":"https://openalex.org/S4363607705","display_name":"GLOBECOM 2022 - 2022 IEEE Global Communications Conference","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"GLOBECOM 2022 - 2022 IEEE Global Communications Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5799999833106995,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1814112028","https://openalex.org/W1999562671","https://openalex.org/W2105906451","https://openalex.org/W2106424475","https://openalex.org/W2137983211","https://openalex.org/W2170736358","https://openalex.org/W2756070521","https://openalex.org/W2989332036","https://openalex.org/W2998540693","https://openalex.org/W3015689570","https://openalex.org/W3038316262","https://openalex.org/W3129572518","https://openalex.org/W3130134189","https://openalex.org/W3136797957","https://openalex.org/W3200827493","https://openalex.org/W4304944461","https://openalex.org/W4311653668","https://openalex.org/W6769952219","https://openalex.org/W6779850432","https://openalex.org/W6790879498","https://openalex.org/W6791882293","https://openalex.org/W6801915000"],"related_works":["https://openalex.org/W2015060724","https://openalex.org/W2919324478","https://openalex.org/W4400665899","https://openalex.org/W2130120519","https://openalex.org/W2012871340","https://openalex.org/W2058578573","https://openalex.org/W2006582835","https://openalex.org/W1973706450","https://openalex.org/W2186864281","https://openalex.org/W2167695847"],"abstract_inverted_index":{"Non-convex":[0],"AC":[1,107],"optimal":[2],"power":[3,12,108,114],"flow":[4,109,115],"(AC-OPF)":[5],"is":[6,21,117],"a":[7,54,59,87,93,130],"fundamental":[8],"optimization":[9],"problem":[10],"in":[11,30],"system":[13],"analysis.":[14],"The":[15,111,139],"computational":[16,123],"complexity":[17],"of":[18,96,148,158],"conventional":[19,67],"solvers":[20,68],"typically":[22],"high":[23],"and":[24],"not":[25],"suitable":[26],"for":[27,83],"large-scale":[28],"networks":[29],"real-time":[31],"operation.":[32],"Hence,":[33],"deep":[34,88],"learning":[35,50,80],"based":[36,81,144],"approaches":[37],"have":[38],"gained":[39],"intensive":[40],"attention":[41],"to":[42,69,91,119],"conduct":[43],"the":[44,71,100,122,136,146,156],"time-consuming":[45],"training":[46,72,137],"process":[47],"offline.":[48],"Supervised":[49],"methods":[51],"may":[52],"yield":[53],"feasible":[55],"AC-OPF":[56],"solution":[57],"with":[58],"small":[60],"optimality":[61],"gap.":[62],"However,":[63],"they":[64],"often":[65],"need":[66],"generate":[70],"dataset.":[73],"This":[74],"paper":[75],"proposes":[76],"an":[77],"end-to-end":[78],"unsupervised":[79],"framework":[82],"AC-OPF.":[84],"We":[85],"develop":[86],"neural":[89],"network":[90],"output":[92],"partial":[94],"set":[95],"decision":[97],"variables":[98,102],"while":[99],"remaining":[101],"are":[103,141],"recovered":[104],"by":[105],"solving":[106],"equations.":[110],"fast":[112],"decoupled":[113],"solver":[116],"adopted":[118],"further":[120],"reduce":[121],"time.":[124],"In":[125],"addition,":[126],"we":[127],"propose":[128],"using":[129],"modified":[131],"augmented":[132],"Lagrangian":[133],"function":[134],"as":[135],"loss.":[138],"multipliers":[140],"adjusted":[142],"dynamically":[143],"on":[145],"degree":[147],"constraint":[149],"violation.":[150],"Extensive":[151],"numerical":[152],"test":[153],"results":[154],"corroborate":[155],"advantages":[157],"our":[159],"proposed":[160],"approach":[161],"over":[162],"some":[163],"existing":[164],"methods.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}