{"id":"https://openalex.org/W3016718084","doi":"https://doi.org/10.1109/tim.2020.2987740","title":"Nonlinear Behavioral Modelling of Voltage Transformers in the Frequency Domain: Comparing Different Approaches","display_name":"Nonlinear Behavioral Modelling of Voltage Transformers in the Frequency Domain: Comparing Different Approaches","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3016718084","doi":"https://doi.org/10.1109/tim.2020.2987740","mag":"3016718084"},"language":"en","primary_location":{"id":"doi:10.1109/tim.2020.2987740","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2020.2987740","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"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 Instrumentation and Measurement","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/A5001972308","display_name":"Marco Faifer","orcid":"https://orcid.org/0000-0002-8777-5444"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Faifer","raw_affiliation_strings":["Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059759550","display_name":"Christian Laurano","orcid":"https://orcid.org/0000-0002-6011-6246"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Christian Laurano","raw_affiliation_strings":["Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017740145","display_name":"Roberto Ottoboni","orcid":"https://orcid.org/0000-0002-5371-1346"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Roberto Ottoboni","raw_affiliation_strings":["Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003675815","display_name":"Sergio Toscani","orcid":"https://orcid.org/0000-0003-2317-5818"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Sergio Toscani","raw_affiliation_strings":["Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064404282","display_name":"Michele Zanoni","orcid":"https://orcid.org/0000-0002-2651-1322"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Michele Zanoni","raw_affiliation_strings":["Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":null,"apc_paid":null,"fwci":0.3317,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.45995318,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11222","display_name":"Magnetic Properties and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11222","display_name":"Magnetic Properties and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10573","display_name":"Power Quality and Harmonics","score":0.9995999932289124,"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/T12300","display_name":"Advanced Electrical Measurement Techniques","score":0.9988999962806702,"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/linearization","display_name":"Linearization","score":0.7783411741256714},{"id":"https://openalex.org/keywords/transfer-function","display_name":"Transfer function","score":0.6982758045196533},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6887195110321045},{"id":"https://openalex.org/keywords/transformer","display_name":"Transformer","score":0.6645481586456299},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.6293958425521851},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.5710554122924805},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5671220421791077},{"id":"https://openalex.org/keywords/frequency-response","display_name":"Frequency response","score":0.5408677458763123},{"id":"https://openalex.org/keywords/volterra-series","display_name":"Volterra series","score":0.5245431065559387},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.48085933923721313},{"id":"https://openalex.org/keywords/harmonic-analysis","display_name":"Harmonic analysis","score":0.45717886090278625},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.4103325605392456},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3831561505794525},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3630300760269165},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.2915342450141907},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1595231592655182},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.136522114276886},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.13306355476379395}],"concepts":[{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.7783411741256714},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.6982758045196533},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6887195110321045},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.6645481586456299},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.6293958425521851},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.5710554122924805},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5671220421791077},{"id":"https://openalex.org/C8590192","wikidata":"https://www.wikidata.org/wiki/Q1054694","display_name":"Frequency response","level":2,"score":0.5408677458763123},{"id":"https://openalex.org/C2778532037","wikidata":"https://www.wikidata.org/wiki/Q3957891","display_name":"Volterra series","level":3,"score":0.5245431065559387},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.48085933923721313},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.45717886090278625},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.4103325605392456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3831561505794525},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3630300760269165},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2915342450141907},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1595231592655182},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.136522114276886},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.13306355476379395},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tim.2020.2987740","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2020.2987740","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"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 Instrumentation and Measurement","raw_type":"journal-article"},{"id":"pmh:oai:re.public.polimi.it:11311/1149893","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/1149893","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.47999998927116394,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W52637353","https://openalex.org/W609997296","https://openalex.org/W612888681","https://openalex.org/W1598535606","https://openalex.org/W1986140267","https://openalex.org/W1988185442","https://openalex.org/W2063409359","https://openalex.org/W2087061179","https://openalex.org/W2093956119","https://openalex.org/W2104100206","https://openalex.org/W2108504544","https://openalex.org/W2125837891","https://openalex.org/W2155329325","https://openalex.org/W2167101944","https://openalex.org/W2294647474","https://openalex.org/W2344463366","https://openalex.org/W2495323230","https://openalex.org/W2518380880","https://openalex.org/W2566778955","https://openalex.org/W2567878791","https://openalex.org/W2587496665","https://openalex.org/W2735547598","https://openalex.org/W2766359152","https://openalex.org/W2795298520","https://openalex.org/W2800238587","https://openalex.org/W2894908605","https://openalex.org/W2896570202","https://openalex.org/W2896644565","https://openalex.org/W2913530567","https://openalex.org/W2946251599","https://openalex.org/W2946361480","https://openalex.org/W2972545697","https://openalex.org/W4285719527","https://openalex.org/W6602111015"],"related_works":["https://openalex.org/W2057635680","https://openalex.org/W2108050916","https://openalex.org/W2546454710","https://openalex.org/W2124130510","https://openalex.org/W2335353069","https://openalex.org/W4298415086","https://openalex.org/W2116202922","https://openalex.org/W1524385089","https://openalex.org/W2032380094","https://openalex.org/W2134520904"],"abstract_inverted_index":{"Instrument":[0],"transformers":[1,55],"suffer":[2],"from":[3,37],"weak":[4],"nonlinearities,":[5],"which":[6],"may":[7],"have":[8],"a":[9,23,28,75],"significant":[10],"impact":[11],"on":[12,22],"harmonic":[13],"measurements.":[14],"Therefore,":[15],"their":[16],"detailed":[17],"characterization":[18],"should":[19],"be":[20,47,101],"based":[21],"nonlinear":[24],"model":[25],"instead":[26],"of":[27,31,53,91,93,111,132],"mere":[29],"measurement":[30],"the":[32,51,82,89,94,104,109,114,126,130],"frequency":[33,60],"response":[34],"function.":[35],"Starting":[36],"this":[38,40],"assumption,":[39],"article":[41],"compares":[42],"different":[43],"models":[44,119],"that":[45,81],"can":[46,100],"employed":[48],"to":[49],"represent":[50],"behavior":[52],"voltage":[54],"(VTs):":[56],"simplified":[57,117],"Volterra":[58,118],"models,":[59],"transfer":[61],"matrixes":[62],"(FTMs),":[63],"and":[64,129],"spectral":[65,105],"linearization":[66,106],"approximation;":[67],"an":[68,122],"inductive":[69],"VT":[70],"has":[71],"been":[72],"considered":[73],"as":[74],"case":[76],"study.":[77],"The":[78],"results":[79],"highlight":[80],"FTM":[83],"approach":[84],"is":[85],"significantly":[86],"affected":[87],"by":[88],"range":[90],"variation":[92],"fundamental":[95],"component,":[96],"while":[97],"remarkable":[98],"accuracy":[99,128],"reached":[102],"with":[103],"approximation":[107],"at":[108],"expense":[110],"complexity.":[112],"On":[113],"other":[115],"hand,":[116],"allow":[120],"obtaining":[121],"effective":[123],"tradeoff":[124],"between":[125],"achieved":[127],"number":[131],"coefficients.":[133]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2020-04-24T00:00:00"}