{"id":"https://openalex.org/W4205117320","doi":"https://doi.org/10.1109/tsg.2021.3139347","title":"Holomorphic Embedding Power Flow Algorithm for Isolated AC Microgrids With Hierarchical Control","display_name":"Holomorphic Embedding Power Flow Algorithm for Isolated AC Microgrids With Hierarchical Control","publication_year":2021,"publication_date":"2021-12-30","ids":{"openalex":"https://openalex.org/W4205117320","doi":"https://doi.org/10.1109/tsg.2021.3139347"},"language":"en","primary_location":{"id":"doi:10.1109/tsg.2021.3139347","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2021.3139347","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":["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/A5045691006","display_name":"Ying Huang","orcid":"https://orcid.org/0000-0002-6589-4397"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ying Huang","raw_affiliation_strings":["State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000319084","display_name":"Xiaomeng Ai","orcid":null},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaomeng Ai","raw_affiliation_strings":["State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027757534","display_name":"Jiakun Fang","orcid":"https://orcid.org/0000-0002-8208-5938"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiakun Fang","raw_affiliation_strings":["State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042732958","display_name":"Shichang Cui","orcid":"https://orcid.org/0000-0001-5568-3038"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shichang Cui","raw_affiliation_strings":["State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046123426","display_name":"Runfeng Zhong","orcid":null},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Runfeng Zhong","raw_affiliation_strings":["State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088298380","display_name":"Wei Yao","orcid":"https://orcid.org/0000-0002-4054-5916"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Yao","raw_affiliation_strings":["State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100641767","display_name":"Jinyu Wen","orcid":"https://orcid.org/0000-0002-0288-727X"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinyu Wen","raw_affiliation_strings":["State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5045691006"],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":0.8319,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.73750737,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"13","issue":"3","first_page":"1679","last_page":"1690"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10223","display_name":"Microgrid Control and Optimization","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10223","display_name":"Microgrid Control and Optimization","score":0.9998999834060669,"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/T10454","display_name":"Optimal Power Flow Distribution","score":0.9951000213623047,"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/T13183","display_name":"Islanding Detection in Power Systems","score":0.9847999811172485,"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/embedding","display_name":"Embedding","score":0.6888691782951355},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5296181440353394},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5259442925453186},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4771123230457306},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4685923457145691},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4341859817504883},{"id":"https://openalex.org/keywords/holomorphic-function","display_name":"Holomorphic function","score":0.42282742261886597},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.42242157459259033},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.4105852544307709},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38535478711128235},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3453042507171631},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.3075876832008362},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1502019464969635},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11240649223327637},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.1015627384185791},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09550550580024719},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08962920308113098},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.07515817880630493}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6888691782951355},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5296181440353394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5259442925453186},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4771123230457306},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4685923457145691},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4341859817504883},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.42282742261886597},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.42242157459259033},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.4105852544307709},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38535478711128235},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3453042507171631},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3075876832008362},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1502019464969635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11240649223327637},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.1015627384185791},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09550550580024719},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08962920308113098},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.07515817880630493},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsg.2021.3139347","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2021.3139347","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.5099999904632568,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G4232463493","display_name":null,"funder_award_id":"52177089","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G658698552","display_name":null,"funder_award_id":"52177088","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1504052325","https://openalex.org/W1984639830","https://openalex.org/W2009704558","https://openalex.org/W2028437657","https://openalex.org/W2041353011","https://openalex.org/W2162273104","https://openalex.org/W2213135968","https://openalex.org/W2319167687","https://openalex.org/W2343971031","https://openalex.org/W2344299036","https://openalex.org/W2405589435","https://openalex.org/W2498647973","https://openalex.org/W2515439609","https://openalex.org/W2575619755","https://openalex.org/W2755439930","https://openalex.org/W2759971529","https://openalex.org/W2783787225","https://openalex.org/W2791002248","https://openalex.org/W2798678637","https://openalex.org/W2808165555","https://openalex.org/W2887694372","https://openalex.org/W2945367416","https://openalex.org/W2954375263","https://openalex.org/W2969772097","https://openalex.org/W2970279233","https://openalex.org/W2984899658","https://openalex.org/W2995449207","https://openalex.org/W2996717309","https://openalex.org/W3004960640","https://openalex.org/W3110261894","https://openalex.org/W3111505148","https://openalex.org/W3138215230","https://openalex.org/W4246401243"],"related_works":["https://openalex.org/W2211201902","https://openalex.org/W3094515845","https://openalex.org/W2982338311","https://openalex.org/W1610978630","https://openalex.org/W4237698157","https://openalex.org/W4386732633","https://openalex.org/W2295512640","https://openalex.org/W2952868792","https://openalex.org/W4226018956","https://openalex.org/W4248409592"],"abstract_inverted_index":{"Power":[0],"flow":[1],"(PF)":[2],"calculation":[3],"plays":[4],"a":[5,19,40,85,89,125],"fundamental":[6],"role":[7],"in":[8,43],"the":[9,46,52,56,63,73,80,139,144],"steady-state":[10],"analysis":[11],"of":[12,55,76,112,143],"isolated":[13,32,77],"microgrids":[14],"(MGs).":[15],"In":[16],"this":[17],"paper,":[18],"novel":[20],"analytical":[21],"PF":[22,82],"algorithm":[23,48],"based":[24],"on":[25,121],"holomorphic":[26],"embedding":[27,44,58],"(HE)":[28],"is":[29,70],"proposed":[30,145],"for":[31],"AC":[33],"MGs":[34],"considering":[35],"hierarchical":[36],"control":[37],"(HC).":[38],"With":[39],"deliberate":[41],"design":[42],"technique,":[45],"presented":[47],"not":[49],"only":[50],"inherits":[51],"deterministic":[53],"property":[54],"canonical":[57],"that":[59],"enables":[60],"to":[61],"derive":[62],"upper-branch":[64],"(operable)":[65],"solution":[66],"explicitly,":[67],"but":[68],"also":[69],"compatible":[71],"with":[72,88],"HC":[74],"characteristic":[75],"MGs.":[78],"Furthermore,":[79],"embedded":[81],"model":[83],"features":[84],"general":[86],"structure":[87],"constant":[90],"recursive":[91],"matrix,":[92],"which":[93],"can":[94],"accommodate":[95],"various":[96],"bus":[97],"types":[98],"and":[99,105,128,132,141],"network":[100],"re-configurations":[101],"(including":[102],"both":[103],"radial":[104],"meshed":[106],"networks),":[107],"as":[108,110],"well":[109],"non-nonlinearities":[111],"voltage-dependent":[113],"load":[114],"models.":[115],"Case":[116],"studies":[117],"are":[118],"carried":[119],"out":[120],"3":[122],"test":[123],"systems:":[124],"12-bus":[126],"MG":[127],"modified":[129],"IEEE":[130],"33-bus":[131],"123-bus":[133],"distribution":[134],"systems.":[135],"Numerical":[136],"results":[137],"reveal":[138],"applicability":[140],"efficacy":[142],"algorithm.":[146]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-04T08:04:53.788161","created_date":"2025-10-10T00:00:00"}