{"id":"https://openalex.org/W2140717263","doi":"https://doi.org/10.1109/tie.2009.2036646","title":"A Space-Vector Discrete Fourier Transform for Unbalanced and Distorted Three-Phase Signals","display_name":"A Space-Vector Discrete Fourier Transform for Unbalanced and Distorted Three-Phase Signals","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W2140717263","doi":"https://doi.org/10.1109/tie.2009.2036646","mag":"2140717263"},"language":"en","primary_location":{"id":"doi:10.1109/tie.2009.2036646","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2009.2036646","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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 Industrial Electronics","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/A5056826429","display_name":"Francisco A. S. Neves","orcid":"https://orcid.org/0000-0003-0564-7500"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]},{"id":"https://openalex.org/I71437568","display_name":"Universidade de Pernambuco","ror":"https://ror.org/00gtcbp88","country_code":"BR","type":"education","lineage":["https://openalex.org/I71437568"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"F A S Neves","raw_affiliation_strings":["Department of Electrical Engineering, Federal University of Pernambuco (UFPE), Recife, Brazil","Dept. of Electr. Eng., Fed. Univ. of Pernambuco, Recife, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Federal University of Pernambuco (UFPE), Recife, Brazil","institution_ids":["https://openalex.org/I25112270"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Fed. Univ. of Pernambuco, Recife, Brazil","institution_ids":["https://openalex.org/I71437568"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045803392","display_name":"Helber E. P. de Souza","orcid":"https://orcid.org/0000-0002-2431-2565"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]},{"id":"https://openalex.org/I71437568","display_name":"Universidade de Pernambuco","ror":"https://ror.org/00gtcbp88","country_code":"BR","type":"education","lineage":["https://openalex.org/I71437568"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"H E P de Souza","raw_affiliation_strings":["Department of Electrical Engineering, Federal University of Pernambuco (UFPE), Recife, Brazil","Dept. of Electr. Eng., Fed. Univ. of Pernambuco, Recife, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Federal University of Pernambuco (UFPE), Recife, Brazil","institution_ids":["https://openalex.org/I25112270"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Fed. Univ. of Pernambuco, Recife, Brazil","institution_ids":["https://openalex.org/I71437568"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014730401","display_name":"Fabr\u00edcio Bradaschia","orcid":"https://orcid.org/0000-0002-2086-7862"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]},{"id":"https://openalex.org/I71437568","display_name":"Universidade de Pernambuco","ror":"https://ror.org/00gtcbp88","country_code":"BR","type":"education","lineage":["https://openalex.org/I71437568"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"F Bradaschia","raw_affiliation_strings":["Department of Electrical Engineering, Federal University of Pernambuco (UFPE), Recife, Brazil","Dept. of Electr. Eng., Fed. Univ. of Pernambuco, Recife, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Federal University of Pernambuco (UFPE), Recife, Brazil","institution_ids":["https://openalex.org/I25112270"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Fed. Univ. of Pernambuco, Recife, Brazil","institution_ids":["https://openalex.org/I71437568"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069182601","display_name":"Marcelo C. Cavalcanti","orcid":"https://orcid.org/0000-0003-0157-0841"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]},{"id":"https://openalex.org/I71437568","display_name":"Universidade de Pernambuco","ror":"https://ror.org/00gtcbp88","country_code":"BR","type":"education","lineage":["https://openalex.org/I71437568"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"M C Cavalcanti","raw_affiliation_strings":["Department of Electrical Engineering, Federal University of Pernambuco (UFPE), Recife, Brazil","Dept. of Electr. Eng., Fed. Univ. of Pernambuco, Recife, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Federal University of Pernambuco (UFPE), Recife, Brazil","institution_ids":["https://openalex.org/I25112270"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Fed. Univ. of Pernambuco, Recife, Brazil","institution_ids":["https://openalex.org/I71437568"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088832489","display_name":"Mario Rizo","orcid":"https://orcid.org/0000-0001-8195-2182"},"institutions":[{"id":"https://openalex.org/I189268942","display_name":"Universidad de Alcal\u00e1","ror":"https://ror.org/04pmn0e78","country_code":"ES","type":"education","lineage":["https://openalex.org/I189268942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M Rizo","raw_affiliation_strings":["Department of Electronics, University of Alcal\u00e1, Alcala de Henares, Spain","Dept. of Electron., Univ. of Alcala, Alcala\u0301 de Henares, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics, University of Alcal\u00e1, Alcala de Henares, Spain","institution_ids":["https://openalex.org/I189268942"]},{"raw_affiliation_string":"Dept. of Electron., Univ. of Alcala, Alcala\u0301 de Henares, Spain","institution_ids":["https://openalex.org/I189268942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100447842","display_name":"Francisco J. Rodr\u00edguez","orcid":"https://orcid.org/0000-0001-8508-1898"},"institutions":[{"id":"https://openalex.org/I189268942","display_name":"Universidad de Alcal\u00e1","ror":"https://ror.org/04pmn0e78","country_code":"ES","type":"education","lineage":["https://openalex.org/I189268942"]},{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR","ES"],"is_corresponding":false,"raw_author_name":"F J Rodriguez","raw_affiliation_strings":["Department of Electrical Engineering, Federal University of Pernambuco (UFPE), Recife, Brazil","Dept. of Electron., Univ. of Alcala, Alcala\u0301 de Henares, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Federal University of Pernambuco (UFPE), Recife, Brazil","institution_ids":["https://openalex.org/I25112270"]},{"raw_affiliation_string":"Dept. of Electron., Univ. of Alcala, Alcala\u0301 de Henares, Spain","institution_ids":["https://openalex.org/I189268942"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.8828,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.95308167,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"57","issue":"8","first_page":"2858","last_page":"2867"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10573","display_name":"Power Quality and Harmonics","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"}},"topics":[{"id":"https://openalex.org/T10573","display_name":"Power Quality and Harmonics","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/T10223","display_name":"Microgrid Control and Optimization","score":0.9983000159263611,"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/T10972","display_name":"Power Systems Fault Detection","score":0.9941999912261963,"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/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.6814177632331848},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.6717284321784973},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6266988515853882},{"id":"https://openalex.org/keywords/harmonic-analysis","display_name":"Harmonic analysis","score":0.6075021624565125},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5897901654243469},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5840545892715454},{"id":"https://openalex.org/keywords/discrete-frequency-domain","display_name":"Discrete frequency domain","score":0.49554193019866943},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49114009737968445},{"id":"https://openalex.org/keywords/discrete-time-fourier-transform","display_name":"Discrete-time Fourier transform","score":0.4503253996372223},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.43759772181510925},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.4132798910140991},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.362190306186676},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.35205864906311035},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.3424985408782959},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.2936711013317108},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2522081136703491},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.21188369393348694},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1345447301864624},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.08771213889122009}],"concepts":[{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.6814177632331848},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.6717284321784973},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6266988515853882},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.6075021624565125},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5897901654243469},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5840545892715454},{"id":"https://openalex.org/C23548689","wikidata":"https://www.wikidata.org/wiki/Q5282049","display_name":"Discrete frequency domain","level":3,"score":0.49554193019866943},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49114009737968445},{"id":"https://openalex.org/C122444316","wikidata":"https://www.wikidata.org/wiki/Q1440048","display_name":"Discrete-time Fourier transform","level":5,"score":0.4503253996372223},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.43759772181510925},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.4132798910140991},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.362190306186676},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.35205864906311035},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.3424985408782959},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.2936711013317108},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2522081136703491},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.21188369393348694},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1345447301864624},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.08771213889122009},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tie.2009.2036646","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2009.2036646","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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 Industrial Electronics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1507884046","https://openalex.org/W1737158314","https://openalex.org/W1766888123","https://openalex.org/W1958699153","https://openalex.org/W2026934209","https://openalex.org/W2043436843","https://openalex.org/W2098782404","https://openalex.org/W2099097596","https://openalex.org/W2100577689","https://openalex.org/W2103457274","https://openalex.org/W2103608196","https://openalex.org/W2110853395","https://openalex.org/W2112106839","https://openalex.org/W2115102890","https://openalex.org/W2127300534","https://openalex.org/W2129842740","https://openalex.org/W2130358341","https://openalex.org/W2132755931","https://openalex.org/W2134666654","https://openalex.org/W2140870634","https://openalex.org/W2143743846","https://openalex.org/W2144081311","https://openalex.org/W2147107167","https://openalex.org/W2153785453","https://openalex.org/W2161547982","https://openalex.org/W2165188326","https://openalex.org/W2171593097","https://openalex.org/W2172212285","https://openalex.org/W2478884216","https://openalex.org/W2533600733","https://openalex.org/W2534519867","https://openalex.org/W2537153402","https://openalex.org/W2563341442"],"related_works":["https://openalex.org/W2118155316","https://openalex.org/W3141389362","https://openalex.org/W198181464","https://openalex.org/W1516606316","https://openalex.org/W4285550727","https://openalex.org/W2154898175","https://openalex.org/W2382218334","https://openalex.org/W2155549970","https://openalex.org/W2128992369","https://openalex.org/W2963406743"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3],"space-vector":[4],"discrete-time":[5],"Fourier":[6,31,58],"transform":[7,32,59],"is":[8,33,49,104,116],"proposed":[9,119],"for":[10,100,110],"fast":[11],"and":[12,18,21,67,112,120,129],"precise":[13],"detection":[14,108],"of":[15,25,64,72,82,93],"the":[16,36,52,57,61,65,73,80,94],"fundamental-frequency":[17,88],"harmonic":[19,69,90],"positive-":[20,66,85],"negative-sequence":[22,68,87],"vector":[23,91],"components":[24],"three-phase":[26,37,75],"input":[27,74,95,114],"signals.":[28,76],"The":[29,77,107,118],"discrete":[30],"applied":[34],"to":[35],"signals":[38,115],"represented":[39],"by":[40],"Clarke's":[41],"<formula":[42],"formulatype=\"inline\"":[43],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[44],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex":[45],"Notation=\"TeX\">$\\alpha\\beta$</tex></formula>":[46],"vector.":[47],"It":[48],"shown":[50],"that":[51],"complex":[53],"numbers":[54],"output":[55],"from":[56],"are":[60,125],"instantaneous":[62],"values":[63],"component":[70,92],"vectors":[71],"method":[78,123],"allows":[79],"computation":[81],"any":[83],"desired":[84],"or":[86,89],"signal.":[96],"A":[97],"recursive":[98],"algorithm":[99],"low-effort":[101],"online":[102],"implementation":[103],"also":[105],"presented.":[106],"performance":[109],"variable-frequency":[111],"interharmonic":[113],"discussed.":[117],"other":[121],"usual":[122],"performances":[124],"compared":[126],"through":[127],"simulations":[128],"experiments.":[130]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}