{"id":"https://openalex.org/W2263004238","doi":"https://doi.org/10.1109/tsg.2017.2715282","title":"Hybrid Methods in Solving Alternating-Current Optimal Power Flows","display_name":"Hybrid Methods in Solving Alternating-Current Optimal Power Flows","publication_year":2017,"publication_date":"2017-06-13","ids":{"openalex":"https://openalex.org/W2263004238","doi":"https://doi.org/10.1109/tsg.2017.2715282","mag":"2263004238"},"language":"en","primary_location":{"id":"doi:10.1109/tsg.2017.2715282","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2017.2715282","pdf_url":null,"source":{"id":"https://openalex.org/S59604973","display_name":"IEEE Transactions on Smart Grid","issn_l":"1949-3053","issn":["1949-3053","1949-3061"],"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 Smart Grid","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1510.02171","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jie Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jie Liu","raw_affiliation_strings":["Lehigh University, Bethlehem, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehigh University, Bethlehem, PA, USA","institution_ids":["https://openalex.org/I186143895"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Alan Claude Liddell","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alan Claude Liddell","raw_affiliation_strings":["University of Notre Dame, South Bend, IN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Notre Dame, South Bend, IN, USA","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jakub Marecek","orcid":"https://orcid.org/0000-0003-0839-0691"},"institutions":[{"id":"https://openalex.org/I4210145784","display_name":"IBM Research - Ireland","ror":"https://ror.org/04jnxr720","country_code":"IE","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4210145784"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Jakub Marecek","raw_affiliation_strings":["IBM Research, Dublin, Ireland"],"raw_orcid":"https://orcid.org/0000-0003-0839-0691","affiliations":[{"raw_affiliation_string":"IBM Research, Dublin, Ireland","institution_ids":["https://openalex.org/I4210145784"]}]},{"author_position":"last","author":{"id":null,"display_name":"Martin Takac","orcid":null},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Martin Takac","raw_affiliation_strings":["Lehigh University, Bethlehem, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehigh University, Bethlehem, PA, USA","institution_ids":["https://openalex.org/I186143895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2672,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.80541214,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"8","issue":"6","first_page":"2988","last_page":"2998"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.7376999855041504,"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":0.7376999855041504,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0778999999165535,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10305","display_name":"Power System Optimization and Stability","score":0.04560000076889992,"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/regular-polygon","display_name":"Regular polygon","score":0.6520000100135803},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5853000283241272},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.5648999810218811},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5339000225067139},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.5199000239372253},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.4765999913215637},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45660001039505005},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.3824999928474426},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.35929998755455017}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6626999974250793},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6520000100135803},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5853000283241272},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.5648999810218811},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5339000225067139},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.5199000239372253},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.4765999913215637},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45660001039505005},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4399999976158142},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.429500013589859},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.3824999928474426},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.35929998755455017},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.35670000314712524},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.34689998626708984},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.33629998564720154},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.32359999418258667},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.3224000036716461},{"id":"https://openalex.org/C2989514635","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization problem","level":3,"score":0.31279999017715454},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2854999899864197},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.25699999928474426},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.2567000091075897},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsg.2017.2715282","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2017.2715282","pdf_url":null,"source":{"id":"https://openalex.org/S59604973","display_name":"IEEE Transactions on Smart Grid","issn_l":"1949-3053","issn":["1949-3053","1949-3061"],"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 Smart Grid","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1510.02171","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.02171","pdf_url":"https://arxiv.org/pdf/1510.02171","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1510.02171","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.02171","pdf_url":"https://arxiv.org/pdf/1510.02171","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7552422871","display_name":null,"funder_award_id":"NSF:CCF:161871","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W91728630","https://openalex.org/W1563228631","https://openalex.org/W1967073510","https://openalex.org/W1980132616","https://openalex.org/W1996702873","https://openalex.org/W1997135619","https://openalex.org/W1999562671","https://openalex.org/W2003298515","https://openalex.org/W2024830592","https://openalex.org/W2028912194","https://openalex.org/W2039353469","https://openalex.org/W2045814149","https://openalex.org/W2051634716","https://openalex.org/W2056822011","https://openalex.org/W2057057063","https://openalex.org/W2071550336","https://openalex.org/W2077223725","https://openalex.org/W2090618049","https://openalex.org/W2092920739","https://openalex.org/W2093909370","https://openalex.org/W2096743478","https://openalex.org/W2104106131","https://openalex.org/W2106424475","https://openalex.org/W2141380252","https://openalex.org/W2141870784","https://openalex.org/W2145367961","https://openalex.org/W2147838503","https://openalex.org/W2156825077","https://openalex.org/W2164944592","https://openalex.org/W2170736358","https://openalex.org/W2248207537","https://openalex.org/W2251458176","https://openalex.org/W2268876679","https://openalex.org/W2292758822","https://openalex.org/W2296530532","https://openalex.org/W2297665473","https://openalex.org/W2327238720","https://openalex.org/W2400408040","https://openalex.org/W2496118591","https://openalex.org/W2963984837","https://openalex.org/W4231804503","https://openalex.org/W6688152854"],"related_works":[],"abstract_inverted_index":{"Many":[0],"steady-state":[1],"problems":[2,24],"in":[3,14],"power":[4,12],"systems,":[5],"including":[6],"rectangular":[7],"power-voltage":[8],"formulations":[9],"of":[10,38,50,66],"optimal":[11],"flows":[13],"the":[15,67],"alternating-current":[16],"model,":[17],"can":[18,30],"be":[19],"cast":[20],"as":[21],"polynomial":[22],"optimization":[23],"(POP).":[25],"For":[26],"a":[27,54,62],"POP,":[28],"one":[29],"derive":[31],"strong":[32],"convex":[33,45,55],"relaxations,":[34],"or":[35],"rather":[36],"hierarchies":[37],"increasingly":[39,42],"strong,":[40],"but":[41],"computationally":[43],"challenging":[44],"relaxations.":[46],"We":[47],"study":[48],"means":[49],"switching":[51],"from":[52],"solving":[53],"relaxation":[56],"to":[57],"Newton's":[58],"method":[59],"working":[60],"on":[61],"non-convex":[63],"(augmented)":[64],"Lagrangian":[65],"POP.":[68]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}