{"id":"https://openalex.org/W2553087624","doi":"https://doi.org/10.1109/allerton.2012.6483274","title":"Global optimization of Optimal Power Flow using a branch & bound algorithm","display_name":"Global optimization of Optimal Power Flow using a branch & bound algorithm","publication_year":2012,"publication_date":"2012-10-01","ids":{"openalex":"https://openalex.org/W2553087624","doi":"https://doi.org/10.1109/allerton.2012.6483274","mag":"2553087624"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2012.6483274","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2012.6483274","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","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/A5060223538","display_name":"Ajit Gopalakrishnan","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ajit Gopalakrishnan","raw_affiliation_strings":["Department of chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038062267","display_name":"Arvind U. Raghunathan","orcid":"https://orcid.org/0000-0003-3173-3875"},"institutions":[{"id":"https://openalex.org/I4210159266","display_name":"Mitsubishi Electric (United States)","ror":"https://ror.org/053jnhe44","country_code":"US","type":"company","lineage":["https://openalex.org/I1306287861","https://openalex.org/I4210133125","https://openalex.org/I4210159266"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arvind U. Raghunathan","raw_affiliation_strings":["Mitsubushi Electric Research Laboratories, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Mitsubushi Electric Research Laboratories, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210159266"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054931604","display_name":"Daniel Nikovski","orcid":"https://orcid.org/0000-0003-2919-645X"},"institutions":[{"id":"https://openalex.org/I4210159266","display_name":"Mitsubishi Electric (United States)","ror":"https://ror.org/053jnhe44","country_code":"US","type":"company","lineage":["https://openalex.org/I1306287861","https://openalex.org/I4210133125","https://openalex.org/I4210159266"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Nikovski","raw_affiliation_strings":["Mitsubushi Electric Research Laboratories, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Mitsubushi Electric Research Laboratories, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210159266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052825722","display_name":"Lorenz T. Biegler","orcid":"https://orcid.org/0000-0003-3875-4441"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lorenz T. Biegler","raw_affiliation_strings":["Department of chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5060223538"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":7.4694,"has_fulltext":false,"cited_by_count":71,"citation_normalized_percentile":{"value":0.97631597,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"609","last_page":"616"},"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":0.9965999722480774,"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":0.9904999732971191,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.6478874087333679},{"id":"https://openalex.org/keywords/global-optimization","display_name":"Global optimization","score":0.6090222001075745},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5939432382583618},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5536469221115112},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5224974751472473},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5016672611236572},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4994800090789795},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.4871515929698944},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.4749472439289093},{"id":"https://openalex.org/keywords/branch-and-bound","display_name":"Branch and bound","score":0.42451778054237366},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.4163973033428192},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41044333577156067},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4033566117286682},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.366905152797699},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.33164650201797485},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.10604986548423767}],"concepts":[{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.6478874087333679},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.6090222001075745},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5939432382583618},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5536469221115112},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5224974751472473},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5016672611236572},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4994800090789795},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.4871515929698944},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.4749472439289093},{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.42451778054237366},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.4163973033428192},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41044333577156067},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4033566117286682},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.366905152797699},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.33164650201797485},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.10604986548423767},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/allerton.2012.6483274","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2012.6483274","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.375.525","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.375.525","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.merl.com/publications/docs/TR2012-088.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.6200000047683716}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W51788365","https://openalex.org/W114465074","https://openalex.org/W224775207","https://openalex.org/W1968878112","https://openalex.org/W1987243715","https://openalex.org/W2004407575","https://openalex.org/W2011970986","https://openalex.org/W2029821157","https://openalex.org/W2062451421","https://openalex.org/W2077230226","https://openalex.org/W2086664392","https://openalex.org/W2100929550","https://openalex.org/W2102674521","https://openalex.org/W2103643667","https://openalex.org/W2104106131","https://openalex.org/W2105906451","https://openalex.org/W2106424475","https://openalex.org/W2116019122","https://openalex.org/W2129146387","https://openalex.org/W2133919892","https://openalex.org/W2134172715","https://openalex.org/W2134869843","https://openalex.org/W2141380252","https://openalex.org/W2154890268","https://openalex.org/W2168283238","https://openalex.org/W2182510773","https://openalex.org/W2536620281","https://openalex.org/W2951444518","https://openalex.org/W4250589301","https://openalex.org/W4297831800"],"related_works":["https://openalex.org/W1971683617","https://openalex.org/W1985053614","https://openalex.org/W1584951881","https://openalex.org/W4245546397","https://openalex.org/W2012183228","https://openalex.org/W2102377323","https://openalex.org/W2367744169","https://openalex.org/W2043301754","https://openalex.org/W2059468126","https://openalex.org/W2962729054"],"abstract_inverted_index":{"We":[0,50,115,138],"propose":[1],"two":[2],"algorithms":[3,18,121,170],"for":[4],"the":[5,8,22,32,41,45,60,64,89,95,103,107,117,120,144,155],"solution":[6],"of":[7,63,94,102,106,119,125],"Optimal":[9],"Power":[10],"Flow":[11],"(OPF)":[12],"problem":[13,66],"to":[14,57,132,143,153,173,177],"global":[15,58,178],"optimality.":[16,179],"The":[17,83,165],"are":[19,130,171],"based":[20],"on":[21,31,88,122],"spatial":[23],"branch":[24,167],"and":[25,72,79,159,168],"bound":[26,169],"framework":[27],"with":[28],"lower":[29],"bounds":[30],"optimal":[33],"objective":[34],"function":[35],"value":[36],"calculated":[37],"by":[38],"solving":[39],"either":[40],"Lagrangian":[42],"dual":[43],"or":[44,91],"semidefinite":[46],"programming":[47],"(SDP)":[48],"relaxation.":[49],"show":[51],"that":[52,147,151],"this":[53],"approach":[54,84],"can":[55],"solve":[56,174],"optimality":[59],"general":[61],"form":[62],"OPF":[65],"including:":[67],"generation":[68],"power":[69,74],"bounds,":[70],"apparent":[71],"real":[73],"line":[75],"limits,":[76],"voltage":[77],"limits":[78],"thermal":[80],"loss":[81],"limits.":[82],"makes":[85],"no":[86],"assumption":[87],"topology":[90],"resistive":[92],"connectivity":[93],"network.":[96],"This":[97],"work":[98],"also":[99,139],"removes":[100],"some":[101],"restrictive":[104],"assumptions":[105],"SDP":[108,156],"approaches":[109],"[1],":[110],"[2],":[111],"[3],":[112],"[4],":[113],"[5].":[114],"present":[116],"performance":[118],"a":[123,134,161],"number":[124],"standard":[126],"IEEE":[127],"systems,":[128],"which":[129],"known":[131],"have":[133,160],"zero":[135],"duality":[136,163],"gap.":[137,164],"make":[140],"parameter":[141],"perturbations":[142],"test":[145],"cases":[146,176],"result":[148],"in":[149],"solutions":[150],"fail":[152],"satisfy":[154],"rank":[157],"condition":[158],"non-zero":[162],"proposed":[166],"able":[172],"these":[175]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":17},{"year":2013,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}