{"id":"https://openalex.org/W4409014215","doi":"https://doi.org/10.1109/access.2025.3556368","title":"A Novel Recursive Methodology for Power Flow Analysis Based on the Holomorphic Embedding Method Using the Total Multiplication of Polynomials","display_name":"A Novel Recursive Methodology for Power Flow Analysis Based on the Holomorphic Embedding Method Using the Total Multiplication of Polynomials","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4409014215","doi":"https://doi.org/10.1109/access.2025.3556368"},"language":"en","primary_location":{"id":"doi:10.1109/access.2025.3556368","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3556368","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2025.3556368","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104143579","display_name":"Glaucus R. S. Lima","orcid":"https://orcid.org/0009-0007-5910-775X"},"institutions":[{"id":"https://openalex.org/I101100930","display_name":"Universidade Federal de Juiz de Fora","ror":"https://ror.org/04yqw9c44","country_code":"BR","type":"education","lineage":["https://openalex.org/I101100930"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Glaucus R. S. Lima","raw_affiliation_strings":["Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil","Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, MG, Brazil"],"raw_orcid":"https://orcid.org/0009-0007-5910-775X","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil","institution_ids":["https://openalex.org/I101100930"]},{"raw_affiliation_string":"Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, MG, Brazil","institution_ids":["https://openalex.org/I101100930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012751846","display_name":"Edimar J. de Oliveira","orcid":"https://orcid.org/0000-0002-7484-034X"},"institutions":[{"id":"https://openalex.org/I101100930","display_name":"Universidade Federal de Juiz de Fora","ror":"https://ror.org/04yqw9c44","country_code":"BR","type":"education","lineage":["https://openalex.org/I101100930"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Edimar J. Oliveira","raw_affiliation_strings":["Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil","Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, MG, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-7484-034X","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil","institution_ids":["https://openalex.org/I101100930"]},{"raw_affiliation_string":"Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, MG, Brazil","institution_ids":["https://openalex.org/I101100930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100780049","display_name":"Leonardo Willer de Oliveira","orcid":"https://orcid.org/0000-0001-9542-8357"},"institutions":[{"id":"https://openalex.org/I101100930","display_name":"Universidade Federal de Juiz de Fora","ror":"https://ror.org/04yqw9c44","country_code":"BR","type":"education","lineage":["https://openalex.org/I101100930"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Leonardo W. Oliveira","raw_affiliation_strings":["Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil","Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, MG, Brazil"],"raw_orcid":"https://orcid.org/0000-0001-9542-8357","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil","institution_ids":["https://openalex.org/I101100930"]},{"raw_affiliation_string":"Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, MG, Brazil","institution_ids":["https://openalex.org/I101100930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081958180","display_name":"Igor D. Melo","orcid":"https://orcid.org/0000-0002-5607-0839"},"institutions":[{"id":"https://openalex.org/I101100930","display_name":"Universidade Federal de Juiz de Fora","ror":"https://ror.org/04yqw9c44","country_code":"BR","type":"education","lineage":["https://openalex.org/I101100930"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Igor D. Melo","raw_affiliation_strings":["Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil","Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, MG, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-5607-0839","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil","institution_ids":["https://openalex.org/I101100930"]},{"raw_affiliation_string":"Department of Electrical Engineering, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, MG, Brazil","institution_ids":["https://openalex.org/I101100930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":1.064,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.73238013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"13","issue":null,"first_page":"59390","last_page":"59404"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9541000127792358,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9541000127792358,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9448999762535095,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9240999817848206,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.7068617343902588},{"id":"https://openalex.org/keywords/holomorphic-function","display_name":"Holomorphic function","score":0.6015329957008362},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5842493772506714},{"id":"https://openalex.org/keywords/power-flow","display_name":"Power flow","score":0.491435170173645},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45297613739967346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44169723987579346},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4405696392059326},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.37664955854415894},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.20660921931266785},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1772960126399994},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0901908278465271},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08847317099571228},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06336808204650879}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7068617343902588},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.6015329957008362},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5842493772506714},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.491435170173645},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45297613739967346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44169723987579346},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4405696392059326},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.37664955854415894},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.20660921931266785},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1772960126399994},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0901908278465271},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08847317099571228},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06336808204650879},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2025.3556368","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3556368","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:53a825a279cf4563ba793f957e910c11","is_oa":true,"landing_page_url":"https://doaj.org/article/53a825a279cf4563ba793f957e910c11","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 13, Pp 59390-59404 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2025.3556368","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3556368","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322980","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais","ror":"https://ror.org/00nc55f03"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1984639830","https://openalex.org/W1999562671","https://openalex.org/W2018943376","https://openalex.org/W2024974584","https://openalex.org/W2030578831","https://openalex.org/W2033579259","https://openalex.org/W2061934070","https://openalex.org/W2066046828","https://openalex.org/W2087070363","https://openalex.org/W2111198155","https://openalex.org/W2144075630","https://openalex.org/W2343971031","https://openalex.org/W2498647973","https://openalex.org/W2783787225","https://openalex.org/W2793863455","https://openalex.org/W2798678637","https://openalex.org/W2801077359","https://openalex.org/W2914438817","https://openalex.org/W2945659197","https://openalex.org/W2952128669","https://openalex.org/W2952435258","https://openalex.org/W2969772097","https://openalex.org/W4205596594","https://openalex.org/W4251014442","https://openalex.org/W4281626758","https://openalex.org/W4294811368","https://openalex.org/W4308690684","https://openalex.org/W4387600512","https://openalex.org/W4404740229"],"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":{"This":[0,59,167],"paper":[1],"introduces":[2],"an":[3,170],"innovative":[4],"recursive":[5,138],"methodology":[6,72],"for":[7,47,76,87,148,158],"ultra-fast":[8],"load":[9,53,199],"flow":[10,54,200],"analysis.":[11],"The":[12,71,128],"approach":[13,60],"is":[14,131,155],"based":[15],"on":[16],"the":[17,26,41,45,52,81,85,98,101,116,122,132,137,152,174,179,186,189,196],"Holomorphic":[18],"Embedding":[19],"Load":[20],"Flow":[21],"Method":[22],"(HELM)":[23],"and":[24,36,121,163],"employs":[25],"Total":[27],"Multiplication":[28],"of":[29,80,100,112,173,181,188],"Polynomials":[30],"(TMP)":[31],"to":[32,68,142,202],"enhance":[33],"computational":[34,65,104,146],"efficiency":[35],"accuracy.":[37],"Unlike":[38],"traditional":[39,197],"HELM,":[40],"proposed":[42,102,153],"procedure":[43],"bypasses":[44],"need":[46,86],"analytical":[48],"continuation,":[49],"directly":[50],"solving":[51],"by":[55],"simple":[56],"polynomial":[57],"multiplication.":[58],"provides":[61],"solutions":[62],"with":[63,93],"reduced":[64,145],"time":[66,147],"compared":[67],"alternative":[69],"methods.":[70],"deduces":[73],"general":[74],"expressions":[75],"calculating":[77],"higher-order":[78,149],"terms":[79],"Maclaurin":[82],"series,":[83],"eliminating":[84],"time-consuming":[88],"matrix":[89],"inversions":[90],"or":[91],"comparisons":[92],"Pad\u00e9":[94],"approximants.":[95],"To":[96],"demonstrate":[97],"effectiveness":[99],"method,":[103],"simulations":[105],"were":[106],"performed":[107],"using":[108],"a":[109,143],"wide":[110],"variety":[111],"test":[113],"systems,":[114],"including":[115,161],"IEEE":[117],"118-bus":[118],"transmission":[119],"system":[120],"equivalent":[123],"476-bus":[124],"Brazilian":[125],"distribution":[126],"system.":[127],"main":[129],"contribution":[130],"TMP":[133],"procedure,":[134],"which":[135],"accelerates":[136],"solution":[139,191],"process.":[140],"Due":[141],"significantly":[144],"term":[150],"calculations,":[151],"method":[154],"well":[156],"suited":[157],"real-time":[159],"applications,":[160],"ill-conditioned":[162],"overloaded":[164],"power":[165],"networks.":[166],"feature":[168],"enables":[169],"accurate":[171],"calculation":[172],"maximum":[175],"loadability":[176],"point":[177],"in":[178,193],"context":[180],"voltage":[182],"stability":[183],"assessment,":[184],"allowing":[185],"determination":[187],"exact":[190],"even":[192],"cases":[194],"where":[195],"Newton-Raphson":[198],"fails":[201],"converge.":[203]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}