{"id":"https://openalex.org/W4205739074","doi":"https://doi.org/10.1109/tcsi.2021.3138515","title":"Modular Multilevel Converter Impedance Computation Based on Periodic Small-Signal Analysis and Vector Fitting","display_name":"Modular Multilevel Converter Impedance Computation Based on Periodic Small-Signal Analysis and Vector Fitting","publication_year":2022,"publication_date":"2022-01-10","ids":{"openalex":"https://openalex.org/W4205739074","doi":"https://doi.org/10.1109/tcsi.2021.3138515"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2021.3138515","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2021.3138515","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11311/1211415","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063714229","display_name":"Davide del Giudice","orcid":"https://orcid.org/0000-0002-7211-5398"},"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":true,"raw_author_name":"Davide del Giudice","raw_affiliation_strings":["Department of Electronics, Information and Bioengineering (DEIB), Politecnico di Milano, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering (DEIB), Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080022239","display_name":"Angelo Brambilla","orcid":"https://orcid.org/0000-0001-9422-6446"},"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":"Angelo Brambilla","raw_affiliation_strings":["Department of Electronics, Information and Bioengineering (DEIB), Politecnico di Milano, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering (DEIB), Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057420531","display_name":"Daniele Linaro","orcid":"https://orcid.org/0000-0001-8751-0350"},"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":"Daniele Linaro","raw_affiliation_strings":["Department of Electronics, Information and Bioengineering (DEIB), Politecnico di Milano, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering (DEIB), Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086093589","display_name":"Federico Bizzarri","orcid":"https://orcid.org/0000-0002-6568-6491"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]},{"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":"Federico Bizzarri","raw_affiliation_strings":["Department of Electronics, Information and Bioengineering (DEIB), Politecnico di Milano, Milan, Italy","Advanced Research Center on Electronic Systems for Information and Communication Technologies \"E. De Castro\" (ARCES), University of Bologna, Bologna, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering (DEIB), Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Advanced Research Center on Electronic Systems for Information and Communication Technologies \"E. De Castro\" (ARCES), University of Bologna, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5063714229"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":null,"apc_paid":null,"fwci":2.117,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.86879823,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"69","issue":"4","first_page":"1832","last_page":"1842"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11102","display_name":"HVDC Systems and Fault Protection","score":0.9998999834060669,"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/T11102","display_name":"HVDC Systems and Fault Protection","score":0.9998999834060669,"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/T14502","display_name":"High-Voltage Power Transmission Systems","score":0.9905999898910522,"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":0.9632999897003174,"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/transfer-function","display_name":"Transfer function","score":0.6260393261909485},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.6035950779914856},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5483697652816772},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5243016481399536},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5240814089775085},{"id":"https://openalex.org/keywords/phasor","display_name":"Phasor","score":0.5061373114585876},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4418075382709503},{"id":"https://openalex.org/keywords/high-voltage-direct-current","display_name":"High-voltage direct current","score":0.43185678124427795},{"id":"https://openalex.org/keywords/equivalent-circuit","display_name":"Equivalent circuit","score":0.43034958839416504},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.4181719720363617},{"id":"https://openalex.org/keywords/electrical-impedance","display_name":"Electrical impedance","score":0.4156414866447449},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.2762523293495178},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2711374759674072},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.22602465748786926},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.2141985297203064},{"id":"https://openalex.org/keywords/direct-current","display_name":"Direct current","score":0.14223968982696533},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10923928022384644},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.10278394818305969}],"concepts":[{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.6260393261909485},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.6035950779914856},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5483697652816772},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5243016481399536},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5240814089775085},{"id":"https://openalex.org/C176605952","wikidata":"https://www.wikidata.org/wiki/Q827674","display_name":"Phasor","level":4,"score":0.5061373114585876},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4418075382709503},{"id":"https://openalex.org/C2781163877","wikidata":"https://www.wikidata.org/wiki/Q370607","display_name":"High-voltage direct current","level":4,"score":0.43185678124427795},{"id":"https://openalex.org/C23572009","wikidata":"https://www.wikidata.org/wiki/Q964981","display_name":"Equivalent circuit","level":3,"score":0.43034958839416504},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4181719720363617},{"id":"https://openalex.org/C17829176","wikidata":"https://www.wikidata.org/wiki/Q179043","display_name":"Electrical impedance","level":2,"score":0.4156414866447449},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.2762523293495178},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2711374759674072},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.22602465748786926},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2141985297203064},{"id":"https://openalex.org/C2776620479","wikidata":"https://www.wikidata.org/wiki/Q159241","display_name":"Direct current","level":3,"score":0.14223968982696533},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10923928022384644},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.10278394818305969},{"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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcsi.2021.3138515","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2021.3138515","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"},{"id":"pmh:oai:re.public.polimi.it:11311/1211415","is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1211415","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:re.public.polimi.it:11311/1211415","is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1211415","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":0.5099999904632568,"display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W623905320","https://openalex.org/W1597944220","https://openalex.org/W1763243278","https://openalex.org/W1908606840","https://openalex.org/W1915388693","https://openalex.org/W1917002007","https://openalex.org/W1983077080","https://openalex.org/W1992528496","https://openalex.org/W1998369000","https://openalex.org/W2021871997","https://openalex.org/W2030160262","https://openalex.org/W2039289383","https://openalex.org/W2059496248","https://openalex.org/W2065367661","https://openalex.org/W2072558413","https://openalex.org/W2080517178","https://openalex.org/W2080673725","https://openalex.org/W2083048944","https://openalex.org/W2100900237","https://openalex.org/W2125614775","https://openalex.org/W2137765946","https://openalex.org/W2143055319","https://openalex.org/W2153597540","https://openalex.org/W2161972857","https://openalex.org/W2171353752","https://openalex.org/W2277054035","https://openalex.org/W2316904322","https://openalex.org/W2486692745","https://openalex.org/W2512653021","https://openalex.org/W2554684021","https://openalex.org/W2582834735","https://openalex.org/W2608954841","https://openalex.org/W2729780364","https://openalex.org/W2746756281","https://openalex.org/W2756945312","https://openalex.org/W2770429053","https://openalex.org/W2779572017","https://openalex.org/W2792970414","https://openalex.org/W2793002279","https://openalex.org/W2802995072","https://openalex.org/W2806559440","https://openalex.org/W2896465235","https://openalex.org/W2903618157","https://openalex.org/W2904583003","https://openalex.org/W2914266160","https://openalex.org/W2937192347","https://openalex.org/W2985587182","https://openalex.org/W3007605815","https://openalex.org/W3011905428","https://openalex.org/W3043944049","https://openalex.org/W3047420179","https://openalex.org/W3082711547","https://openalex.org/W3088862700","https://openalex.org/W3090827091","https://openalex.org/W3093889505","https://openalex.org/W3100243383","https://openalex.org/W3109081469","https://openalex.org/W3119407092","https://openalex.org/W3158548735","https://openalex.org/W4205232303","https://openalex.org/W4233863580","https://openalex.org/W6681202601","https://openalex.org/W6749659822"],"related_works":["https://openalex.org/W2071137974","https://openalex.org/W4224280502","https://openalex.org/W2503196393","https://openalex.org/W2166008706","https://openalex.org/W2127773678","https://openalex.org/W1923806246","https://openalex.org/W2543747607","https://openalex.org/W2165286486","https://openalex.org/W1768317165","https://openalex.org/W2170523068"],"abstract_inverted_index":{"Instability":[0],"and":[1,56,81,162],"oscillation":[2],"issues":[3],"originating":[4],"in":[5,20,28,64,138,185],"high-voltage":[6],"direct":[7],"current":[8],"(HVDC)":[9],"systems":[10],"comprising":[11],"modular":[12],"multilevel":[13],"converters":[14],"(MMCs)":[15],"are":[16],"gaining":[17],"increasing":[18],"interest":[19],"the":[21,54,94,122,126,139],"research":[22],"community.":[23],"To":[24,70,170],"detect":[25,182],"such":[26,46],"phenomena":[27],"advance,":[29],"considerable":[30],"effort":[31],"has":[32],"been":[33],"devoted":[34],"recently":[35],"to":[36,53,101,124,131,150,159,181],"developing":[37],"MMC":[38,129],"models":[39,47],"for":[40],"small-signal":[41,96],"analysis.":[42],"The":[43],"derivation":[44],"of":[45,60,177],"is":[48,99],"a":[49,67,133,186],"challenging":[50],"task":[51],"due":[52],"topology":[55],"complex":[57],"control":[58],"structure":[59],"MMCs,":[61],"which":[62,154],"results":[63],"them":[65],"having":[66],"multi-frequency":[68],"response.":[69],"address":[71],"this":[72,92,172],"issue,":[73],"scholars":[74],"developed":[75],"methods":[76],"based":[77],"on":[78],"dynamic":[79],"phasors":[80],"harmonic":[82],"state-space":[83],"modelling,":[84],"which,":[85],"however,":[86],"require":[87],"extensive":[88],"pen-and-paper":[89],"computations.":[90],"In":[91],"paper,":[93],"periodic":[95],"analysis":[97],"(PAC)":[98],"adopted":[100],"determine":[102],"numerically":[103],"several":[104],"MMCs":[105,161],"transfer":[106,179],"functions.":[107],"Such":[108],"functions":[109,149,180],"can":[110,155],"be":[111,156],"computed":[112],"between":[113],"any":[114],"electrical":[115],"circuit":[116],"node":[117],"or":[118],"input/output":[119],"port,":[120],"without":[121],"need":[123],"recast":[125],"three-phase":[127],"average":[128],"model":[130],"derive":[132],"linear":[134],"equivalent":[135,151],"one,":[136],"possibly":[137],"DQ-frame.":[140],"We":[141],"show":[142],"how":[143],"vector":[144],"fitting":[145],"allows":[146],"converting":[147],"these":[148,178],"algebraic":[152],"representations,":[153],"profitably":[157],"used":[158],"design":[160],"study":[163],"their":[164],"stability":[165],"following":[166],"some":[167],"parameter":[168],"changes.":[169],"showcase":[171],"feature,":[173],"we":[174],"exploit":[175],"one":[176],"DC-side":[183],"instability":[184],"point-to-point":[187],"HVDC":[188],"system.":[189]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5}],"updated_date":"2026-03-29T08:15:47.926485","created_date":"2022-01-26T00:00:00"}