{"id":"https://openalex.org/W4210728769","doi":"https://doi.org/10.1109/cdc45484.2021.9683780","title":"Linearized Three-Phase Optimal Power Flow Models for Distribution Grids with Voltage Unbalance","display_name":"Linearized Three-Phase Optimal Power Flow Models for Distribution Grids with Voltage Unbalance","publication_year":2021,"publication_date":"2021-12-14","ids":{"openalex":"https://openalex.org/W4210728769","doi":"https://doi.org/10.1109/cdc45484.2021.9683780"},"language":"en","primary_location":{"id":"doi:10.1109/cdc45484.2021.9683780","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc45484.2021.9683780","pdf_url":null,"source":{"id":"https://openalex.org/S4363607724","display_name":"2021 60th IEEE Conference on Decision and Control (CDC)","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":"2021 60th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5013253430","display_name":"Kshitij Girigoudar","orcid":"https://orcid.org/0000-0002-7683-3338"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kshitij Girigoudar","raw_affiliation_strings":["University of Wisconsin-Madison,Department of Electrical and Computer Engineering,USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison,Department of Electrical and Computer Engineering,USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005034793","display_name":"Line Roald","orcid":"https://orcid.org/0000-0003-4378-7272"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Line A. Roald","raw_affiliation_strings":["University of Wisconsin-Madison,Department of Electrical and Computer Engineering,USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison,Department of Electrical and Computer Engineering,USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"4214","last_page":"4221"},"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/T10223","display_name":"Microgrid Control and Optimization","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10603","display_name":"Smart Grid Energy Management","score":0.9948999881744385,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.66357421875},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5895335674285889},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.5858179330825806},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5374889969825745},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4686664342880249},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.44185787439346313},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4358293116092682},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3955593705177307},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3626001477241516},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25020503997802734},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07730036973953247}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.66357421875},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5895335674285889},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.5858179330825806},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5374889969825745},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4686664342880249},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.44185787439346313},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4358293116092682},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3955593705177307},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3626001477241516},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25020503997802734},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07730036973953247},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc45484.2021.9683780","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc45484.2021.9683780","pdf_url":null,"source":{"id":"https://openalex.org/S4363607724","display_name":"2021 60th IEEE Conference on Decision and Control (CDC)","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":"2021 60th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8899999856948853}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W51886086","https://openalex.org/W1571403844","https://openalex.org/W1918816242","https://openalex.org/W1963539491","https://openalex.org/W1984802760","https://openalex.org/W2002694899","https://openalex.org/W2011393317","https://openalex.org/W2058937311","https://openalex.org/W2063559372","https://openalex.org/W2120575449","https://openalex.org/W2123871098","https://openalex.org/W2133919892","https://openalex.org/W2141380252","https://openalex.org/W2157726340","https://openalex.org/W2160935860","https://openalex.org/W2163915223","https://openalex.org/W2182958716","https://openalex.org/W2461951329","https://openalex.org/W2552962666","https://openalex.org/W2620296980","https://openalex.org/W2762654164","https://openalex.org/W2889222609","https://openalex.org/W2922251527","https://openalex.org/W2963059498","https://openalex.org/W2964100695","https://openalex.org/W3049217260","https://openalex.org/W3100598929","https://openalex.org/W3104243370","https://openalex.org/W3105558219","https://openalex.org/W3105577550","https://openalex.org/W4296139939","https://openalex.org/W4297733574","https://openalex.org/W6718109608"],"related_works":["https://openalex.org/W2390714398","https://openalex.org/W2915885076","https://openalex.org/W1973822606","https://openalex.org/W2371730979","https://openalex.org/W2762148993","https://openalex.org/W2348350842","https://openalex.org/W2112452310","https://openalex.org/W2149579383","https://openalex.org/W3005998369","https://openalex.org/W2083669091"],"abstract_inverted_index":{"One":[0],"of":[1,22,33,77,152],"the":[2,34,67,96,117,147,153,166,189,194,208,222],"major":[3],"challenges":[4],"to":[5,94,135,171,219],"efficiently":[6],"solving":[7],"an":[8,123,130],"optimal":[9],"power":[10,119,224],"flow":[11,120,225],"(OPF)":[12],"problem":[13],"for":[14,40,48,75,122],"large-scale,":[15],"unbalanced":[16],"distribution":[17,41],"grids":[18],"with":[19,177,188],"high":[20,172],"penetration":[21],"distributed":[23],"energy":[24],"resources":[25],"is":[26,201],"computation":[27,181],"time.":[28,182],"Although":[29],"various":[30],"convex":[31],"relaxations":[32,59],"OPF":[35],"problems":[36],"have":[37],"been":[38],"proposed":[39,154],"grids,":[42],"they":[43],"do":[44,89],"not":[45,90],"scale":[46],"well":[47],"large":[49,158],"networks":[50],"or":[51,126],"guarantee":[52],"solutions":[53,139,176,185],"that":[54,88,207],"are":[55,102,186],"AC":[56,118,137,174,223],"feasible.":[57],"Many":[58],"and":[60,110,149],"linear":[61],"approximations":[62],"make":[63,91],"limiting":[64],"assumptions":[65,93],"on":[66,104,198],"relationship":[68],"between":[69],"phase":[70],"voltages,":[71],"making":[72],"them":[73],"unsuitable":[74],"analysis":[76],"voltage":[78],"unbalance.":[79],"In":[80],"this":[81],"paper,":[82],"we":[83,145],"utilize":[84],"three":[85,164,209],"linearized":[86],"formulations":[87],"such":[92],"reduce":[95],"computational":[97],"complexity.":[98],"These":[99],"linearizations,":[100,165],"which":[101],"based":[103,197],"first-order":[105,190],"Taylor":[106,191],"expansion,":[107,192],"fixed-point":[108],"equation":[109],"forward-backward":[111,199],"sweep,":[112],"can":[113],"either":[114],"directly":[115,220],"replace":[116,221],"constraints":[121],"approximate":[124],"solution":[125,150],"be":[127],"incorporated":[128],"in":[129,180],"iterative,":[131],"successive":[132,167],"approximation":[133,168,213],"scheme":[134,169],"yield":[136],"feasible":[138,175],"upon":[140],"convergence.":[141],"For":[142,162],"our":[143],"analysis,":[144],"test":[146],"scalability":[148],"quality":[151],"strategies":[155],"using":[156],"a":[157],"1833-bus":[159],"taxonomic":[160],"feeder.":[161],"all":[163],"converges":[170],"quality,":[173],"significant":[178],"improvement":[179],"The":[183],"best":[184],"obtained":[187],"but":[193],"iterative":[195],"method":[196],"sweep":[200],"significantly":[202],"faster.":[203],"We":[204],"further":[205],"observe":[206],"linearizations":[210],"provide":[211],"better":[212],"accuracy":[214],"than":[215],"Lin3DistFlow":[216],"when":[217],"used":[218],"constraints.":[226]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}