{"id":"https://openalex.org/W4415954360","doi":"https://doi.org/10.1109/access.2026.3672335","title":"Small-Signal Stability Analysis of Power Systems by Implicit Multilinear Models","display_name":"Small-Signal Stability Analysis of Power Systems by Implicit Multilinear Models","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W4415954360","doi":"https://doi.org/10.1109/access.2026.3672335"},"language":"en","primary_location":{"id":"doi:10.1109/access.2026.3672335","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2026.3672335","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":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2026.3672335","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067899718","display_name":"Christoph Kaufmann","orcid":"https://orcid.org/0000-0002-0666-1104"},"institutions":[{"id":"https://openalex.org/I4210124112","display_name":"Fraunhofer Institute for Wind Energy Systems","ror":"https://ror.org/02phevt59","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210124112","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christoph Kaufmann","raw_affiliation_strings":["Application Center for Integration of Local Energy Systems ILES, Fraunhofer Institute for Wind Energy Systems IWES, Bremerhaven, Germany"],"raw_orcid":"https://orcid.org/0000-0002-0666-1104","affiliations":[{"raw_affiliation_string":"Application Center for Integration of Local Energy Systems ILES, Fraunhofer Institute for Wind Energy Systems IWES, Bremerhaven, Germany","institution_ids":["https://openalex.org/I4210124112"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085311250","display_name":"Georg Pangalos","orcid":"https://orcid.org/0000-0001-5094-8033"},"institutions":[{"id":"https://openalex.org/I4210124112","display_name":"Fraunhofer Institute for Wind Energy Systems","ror":"https://ror.org/02phevt59","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210124112","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Georg Pangalos","raw_affiliation_strings":["Application Center for Integration of Local Energy Systems ILES, Fraunhofer Institute for Wind Energy Systems IWES, Bremerhaven, Germany"],"raw_orcid":"https://orcid.org/0000-0001-5094-8033","affiliations":[{"raw_affiliation_string":"Application Center for Integration of Local Energy Systems ILES, Fraunhofer Institute for Wind Energy Systems IWES, Bremerhaven, Germany","institution_ids":["https://openalex.org/I4210124112"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004305934","display_name":"Gerwald Lichtenberg","orcid":"https://orcid.org/0000-0001-6032-0733"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I70451448","display_name":"HAW Hamburg","ror":"https://ror.org/00fkqwx76","country_code":"DE","type":"education","lineage":["https://openalex.org/I70451448"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gerwald Lichtenberg","raw_affiliation_strings":["Faculty Life Sciences, Hamburg University of Applied Sciences, Hamburg, Germany"],"raw_orcid":"https://orcid.org/0000-0001-6032-0733","affiliations":[{"raw_affiliation_string":"Faculty Life Sciences, Hamburg University of Applied Sciences, Hamburg, Germany","institution_ids":["https://openalex.org/I70451448","https://openalex.org/I159176309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091210916","display_name":"Oriol Gomis\u2010Bellmunt","orcid":"https://orcid.org/0000-0002-9507-8278"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Oriol Gomis-Bellmunt","raw_affiliation_strings":["Departament d’Enginyeria Elèctrica, Centre d’Innovació Tecnológica en Convertidors Estàtics i Accionaments, Universitat Politècnica de Catalunya, Barcelona, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9507-8278","affiliations":[{"raw_affiliation_string":"Departament d’Enginyeria Elèctrica, Centre d’Innovació Tecnológica en Convertidors Estàtics i Accionaments, Universitat Politècnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":2,"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":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00667088,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":null,"first_page":"37951","last_page":"37967"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10305","display_name":"Power System Optimization and Stability","score":0.8791000247001648,"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/T10305","display_name":"Power System Optimization and Stability","score":0.8791000247001648,"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":0.032499998807907104,"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/T12303","display_name":"Tensor decomposition and applications","score":0.020899999886751175,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multilinear-map","display_name":"Multilinear map","score":0.9714000225067139},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.6851999759674072},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5837000012397766},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5590000152587891},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5389999747276306},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5175999999046326},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.47769999504089355},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.45750001072883606}],"concepts":[{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.9714000225067139},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6872000098228455},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.6851999759674072},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5837000012397766},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5662000179290771},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5590000152587891},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5389999747276306},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5175999999046326},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.47769999504089355},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.45750001072883606},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.38040000200271606},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.37610000371932983},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3659000098705292},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31630000472068787},{"id":"https://openalex.org/C60321788","wikidata":"https://www.wikidata.org/wiki/Q1197190","display_name":"Multilinear algebra","level":5,"score":0.296099990606308},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2637999951839447},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1109/access.2026.3672335","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2026.3672335","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:arXiv.org:2510.16534","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.16534","pdf_url":"https://arxiv.org/pdf/2510.16534","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:doi:10.48550/arxiv.2510.16534","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:17276927eac24343b89ef0991c6237e7","is_oa":true,"landing_page_url":"https://doaj.org/article/17276927eac24343b89ef0991c6237e7","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 14, Pp 37951-37967 (2026)","raw_type":"article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/511577","is_oa":true,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/511577","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"},{"id":"pmh:oai:upcommons.upc.edu:2117/462291","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/462291","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2510.16534","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.16534","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1109/access.2026.3672335","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2026.3672335","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":[{"id":"https://openalex.org/G210044653","display_name":null,"funder_award_id":"03EI4095","funder_id":"https://openalex.org/F4320323803","funder_display_name":"Bundesministerium f\u00fcr Wirtschaft und Energie"},{"id":"https://openalex.org/G4831409948","display_name":"Advanced Grid Interfaces for innovative STorage INtegration","funder_award_id":"101096197","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5350190819","display_name":null,"funder_award_id":"101 069750","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322121","display_name":"Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats","ror":"https://ror.org/0371hy230"},{"id":"https://openalex.org/F4320323803","display_name":"Bundesministerium f\u00fcr Wirtschaft und Energie","ror":"https://ror.org/02vgg2808"},{"id":"https://openalex.org/F4320334322","display_name":"HORIZON EUROPE Framework Programme","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,51,61],"paper":[1,62],"proposes":[2],"a":[3,150],"new":[4],"approach":[5,95],"to":[6,154],"perform":[7],"small-signal":[8,64],"stability":[9,65],"analysis":[10,66],"based":[11,70],"on":[12,71],"linearization":[13,152],"of":[14,27,36,55,67,87,110,117,130,143],"implicit":[15,72,90,112,145],"multilinear":[16,25,73,91,113,146],"models.":[17],"Multilinear":[18],"models":[19,74,86],"describe":[20],"the":[21,88,111,118,125,131,139,144],"system":[22,102],"dynamics":[23],"by":[24,106,123],"functions":[26],"state,":[28],"input,":[29],"and":[30,57,121],"algebraic":[31],"variables.":[32],"Using":[33],"suitable":[34],"transformations":[35],"variables,":[37],"they":[38],"can":[39],"also":[40],"represent":[41],"trigonometric":[42],"functions,":[43],"which":[44],"often":[45],"occur":[46],"in":[47,157],"power":[48,59,101],"systems":[49],"modeling.":[50],"allows":[52,148],"tensor":[53,141],"representations":[54],"grid-following":[56],"grid-forming":[58],"converters.":[60],"introduces":[63],"equilibrium":[68],"points":[69],"using":[75,98],"generalized":[76,79,126],"eigenvalues.":[77],"The":[78,93,135],"eigenvalues":[80,127],"are":[81],"computed":[82],"from":[83],"linear":[84],"descriptor":[85],"linearized":[89,132],"model.":[92,134],"proposed":[94],"is":[96],"tested":[97],"an":[99],"essential":[100],"network":[103],"example,":[104],"first":[105],"comparing":[107,124],"time-domain":[108],"simulations":[109],"model":[114,147],"with":[115,128],"those":[116,129],"nonlinear":[119,133],"model,":[120],"second":[122],"results":[136],"show":[137],"that":[138],"decomposed":[140],"representation":[142],"for":[149],"faster":[151],"compared":[153],"conventional":[155],"methods":[156],"MATLAB":[158],"Simulink.":[159]},"counts_by_year":[],"updated_date":"2026-07-11T18:08:03.149640","created_date":"2025-10-22T00:00:00"}