{"id":"https://openalex.org/W3010443530","doi":"https://doi.org/10.1109/jsyst.2020.2971838","title":"Multiobjective Optimal Power Flow Using a Semidefinite Programming-Based Model","display_name":"Multiobjective Optimal Power Flow Using a Semidefinite Programming-Based Model","publication_year":2020,"publication_date":"2020-03-03","ids":{"openalex":"https://openalex.org/W3010443530","doi":"https://doi.org/10.1109/jsyst.2020.2971838","mag":"3010443530"},"language":"en","primary_location":{"id":"doi:10.1109/jsyst.2020.2971838","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsyst.2020.2971838","pdf_url":null,"source":{"id":"https://openalex.org/S95999327","display_name":"IEEE Systems Journal","issn_l":"1932-8184","issn":["1932-8184","1937-9234","2373-7816"],"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 Systems Journal","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://osuva.uwasa.fi/bitstream/10024/10726/2/Osuva_Davoodi_ym_2020.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079220269","display_name":"Elnaz Davoodi","orcid":"https://orcid.org/0000-0003-3347-2904"},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Elnaz Davoodi","raw_affiliation_strings":["Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran"],"affiliations":[{"raw_affiliation_string":"Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042643606","display_name":"Ebrahim Babaei","orcid":"https://orcid.org/0000-0003-1460-5177"},"institutions":[{"id":"https://openalex.org/I69050122","display_name":"Near East University","ror":"https://ror.org/02x8svs93","country_code":"CY","type":"education","lineage":["https://openalex.org/I69050122"]},{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["CY","IR"],"is_corresponding":false,"raw_author_name":"Ebrahim Babaei","raw_affiliation_strings":["Engineering Faculty, Near East University, Nicosia, Turkey","Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran"],"affiliations":[{"raw_affiliation_string":"Engineering Faculty, Near East University, Nicosia, Turkey","institution_ids":["https://openalex.org/I69050122"]},{"raw_affiliation_string":"Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016541935","display_name":"Behnam Mohammadi\u2010Ivatloo","orcid":"https://orcid.org/0000-0002-0255-8353"},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]},{"id":"https://openalex.org/I170238339","display_name":"Duy Tan University","ror":"https://ror.org/05ezss144","country_code":"VN","type":"education","lineage":["https://openalex.org/I170238339"]}],"countries":["IR","VN"],"is_corresponding":false,"raw_author_name":"Behnam Mohammadi-Ivatloo","raw_affiliation_strings":["Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran","Institute of Research and Development, Duy Tan University, Da Nang, Vietnam"],"affiliations":[{"raw_affiliation_string":"Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]},{"raw_affiliation_string":"Institute of Research and Development, Duy Tan University, Da Nang, Vietnam","institution_ids":["https://openalex.org/I170238339"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088560163","display_name":"Miadreza Shafie\u2010khah","orcid":"https://orcid.org/0000-0003-1691-5355"},"institutions":[{"id":"https://openalex.org/I79765343","display_name":"University of Vaasa","ror":"https://ror.org/03769b225","country_code":"FI","type":"education","lineage":["https://openalex.org/I79765343"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Miadreza Shafie-Khah","raw_affiliation_strings":["School of Technology and Innovations, University of Vaasa, Vaasa, Finland"],"affiliations":[{"raw_affiliation_string":"School of Technology and Innovations, University of Vaasa, Vaasa, Finland","institution_ids":["https://openalex.org/I79765343"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065382518","display_name":"Jo\u00e3o P. S. Catal\u00e0o","orcid":"https://orcid.org/0000-0002-2105-3051"},"institutions":[{"id":"https://openalex.org/I4210166615","display_name":"INESC TEC","ror":"https://ror.org/05fa8ka61","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210125590","https://openalex.org/I4210166615"]},{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Joao P. S. Catalao","raw_affiliation_strings":["Faculty of Engineering, Institute for Systems and Computer Engineering, Technology and Science, University of Porto, Porto, Portugal"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Institute for Systems and Computer Engineering, Technology and Science, University of Porto, Porto, Portugal","institution_ids":["https://openalex.org/I4210166615","https://openalex.org/I182534213"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5079220269"],"corresponding_institution_ids":["https://openalex.org/I41832843"],"apc_list":null,"apc_paid":null,"fwci":1.5596,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.82773581,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"1","first_page":"158","last_page":"169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":1.0,"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":1.0,"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/T10424","display_name":"Electric Power System Optimization","score":0.9994000196456909,"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":0.9983999729156494,"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":0.7914376854896545},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.6782959699630737},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.5408135056495667},{"id":"https://openalex.org/keywords/power-flow","display_name":"Power flow","score":0.523646354675293},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.49921298027038574},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.49630647897720337},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.4807131588459015},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47890105843544006},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.45025789737701416},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.3475172519683838},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.3108275830745697},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2851775288581848}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7914376854896545},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.6782959699630737},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.5408135056495667},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.523646354675293},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.49921298027038574},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.49630647897720337},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4807131588459015},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47890105843544006},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.45025789737701416},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.3475172519683838},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3108275830745697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2851775288581848},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","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},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/jsyst.2020.2971838","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsyst.2020.2971838","pdf_url":null,"source":{"id":"https://openalex.org/S95999327","display_name":"IEEE Systems Journal","issn_l":"1932-8184","issn":["1932-8184","1937-9234","2373-7816"],"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 Systems Journal","raw_type":"journal-article"},{"id":"pmh:oai:osuva.uwasa.fi:10024/10726","is_oa":true,"landing_page_url":"https://osuva.uwasa.fi/handle/10024/10726","pdf_url":"https://osuva.uwasa.fi/bitstream/10024/10726/2/Osuva_Davoodi_ym_2020.pdf","source":{"id":"https://openalex.org/S4306400974","display_name":"Osuva (University of Vaasa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79765343","host_organization_name":"University of Vaasa","host_organization_lineage":["https://openalex.org/I79765343"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:osuva.uwasa.fi:10024/10726","is_oa":true,"landing_page_url":"https://osuva.uwasa.fi/handle/10024/10726","pdf_url":"https://osuva.uwasa.fi/bitstream/10024/10726/2/Osuva_Davoodi_ym_2020.pdf","source":{"id":"https://openalex.org/S4306400974","display_name":"Osuva (University of Vaasa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79765343","host_organization_name":"University of Vaasa","host_organization_lineage":["https://openalex.org/I79765343"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.6499999761581421,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3010443530.pdf","grobid_xml":"https://content.openalex.org/works/W3010443530.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W194786220","https://openalex.org/W572922989","https://openalex.org/W1978496689","https://openalex.org/W1994105715","https://openalex.org/W1994782139","https://openalex.org/W2004158676","https://openalex.org/W2006983488","https://openalex.org/W2008502073","https://openalex.org/W2017963665","https://openalex.org/W2019772850","https://openalex.org/W2026662237","https://openalex.org/W2053074949","https://openalex.org/W2057332356","https://openalex.org/W2058031044","https://openalex.org/W2061822764","https://openalex.org/W2074527871","https://openalex.org/W2094287934","https://openalex.org/W2116596943","https://openalex.org/W2121876331","https://openalex.org/W2126105956","https://openalex.org/W2130400949","https://openalex.org/W2141380252","https://openalex.org/W2164287357","https://openalex.org/W2170540951","https://openalex.org/W2319782977","https://openalex.org/W2326339002","https://openalex.org/W2342670544","https://openalex.org/W2401164885","https://openalex.org/W2603019852","https://openalex.org/W2604438643","https://openalex.org/W2610880365","https://openalex.org/W2679560930","https://openalex.org/W2945580762","https://openalex.org/W2945932644","https://openalex.org/W2951963162","https://openalex.org/W4250589301","https://openalex.org/W4301821551"],"related_works":["https://openalex.org/W2090178682","https://openalex.org/W4241467429","https://openalex.org/W2001591765","https://openalex.org/W2073147994","https://openalex.org/W2770440678","https://openalex.org/W2384474142","https://openalex.org/W3083133203","https://openalex.org/W1588199609","https://openalex.org/W2744462909","https://openalex.org/W1971520370"],"abstract_inverted_index":{"In":[0],"spite":[1],"of":[2,10,17,45,91,160,170],"the":[3,8,18,23,40,48,68,78,89,92,129,135,151,158,167,173,177],"significant":[4],"advance":[5],"achieved":[6],"in":[7,22,28,47,142,164],"development":[9],"optimal":[11,103],"power":[12],"flow":[13],"(OPF)":[14],"programs,":[15],"most":[16],"solution":[19,159,180],"methods":[20,154],"reported":[21],"literature":[24],"have":[25],"considerable":[26],"difficulties":[27],"dealing":[29],"with":[30,105,121,138,166],"different-nature":[31],"objective":[32,80],"functions":[33,81],"simultaneously.":[34],"By":[35],"leveraging":[36],"recent":[37],"progress":[38],"on":[39,54,110],"semidefinite":[41],"programming":[42],"(SDP)":[43],"relaxations":[44],"OPF,":[46],"present":[49],"article,":[50],"attention":[51],"is":[52],"focused":[53],"modeling":[55],"a":[56,73],"new":[57],"SDP-based":[58,93],"multiobjective":[59],"OPF":[60,65],"(MO-OPF)":[61],"problem.":[62],"The":[63],"proposed":[64,130],"model":[66,94,132],"incorporates":[67],"classical":[69],"\u03b5-constraint":[70],"approach":[71],"through":[72],"parameterization":[74],"strategy":[75],"to":[76,98],"handle":[77],"multiple":[79],"and":[82,115,124,149,186,191],"produce":[83,134],"Pareto":[84,102,147],"front.":[85],"This":[86],"article":[87],"emphasizes":[88],"extension":[90],"for":[95,157,172],"MO-OPF":[96],"problems":[97],"generate":[99,145],"globally":[100],"nondominated":[101,136],"solutions":[104,137],"uniform":[106],"distribution.":[107],"Numerical":[108],"results":[109,169],"IEEE":[111],"30-,":[112],"57-,":[113],"118-bus,":[114],"Indian":[116],"utility":[117],"62-bus":[118],"test":[119,175],"systems":[120],"all":[122],"security":[123],"operating":[125],"constraints":[126],"show":[127],"that":[128],"convex":[131],"can":[133],"no":[139],"duality":[140],"gap":[141],"polynomial":[143],"time,":[144],"efficient":[146],"set,":[148],"outperform":[150],"well-known":[152],"heuristic":[153],"generally":[155],"used":[156],"MO-OPF.":[161],"For":[162],"instance,":[163],"comparison":[165],"obtained":[168,181],"NSGA-II":[171],"57-bus":[174],"system,":[176],"best":[178],"compromise":[179],"by":[182],"SDP":[183],"has":[184],"1.55%":[185],"7.42%":[187],"less":[188],"fuel":[189],"cost":[190],"transmission":[192],"losses,":[193],"respectively.":[194]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}