{"id":"https://openalex.org/W2755451687","doi":"https://doi.org/10.1109/tsg.2017.2752146","title":"Nonlinear Lyapunov Stability Analysis of Seven Models of a DC/AC Droop Controlled Inverter Connected to an Infinite Bus","display_name":"Nonlinear Lyapunov Stability Analysis of Seven Models of a DC/AC Droop Controlled Inverter Connected to an Infinite Bus","publication_year":2017,"publication_date":"2017-09-13","ids":{"openalex":"https://openalex.org/W2755451687","doi":"https://doi.org/10.1109/tsg.2017.2752146","mag":"2755451687"},"language":"en","primary_location":{"id":"doi:10.1109/tsg.2017.2752146","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2017.2752146","pdf_url":null,"source":{"id":"https://openalex.org/S59604973","display_name":"IEEE Transactions on Smart Grid","issn_l":"1949-3053","issn":["1949-3053","1949-3061"],"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 Smart Grid","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/A5054338568","display_name":"Mahmoud Kabalan","orcid":"https://orcid.org/0000-0002-0113-1841"},"institutions":[{"id":"https://openalex.org/I161515732","display_name":"University of St. Thomas - Minnesota","ror":"https://ror.org/05vfxvp80","country_code":"US","type":"education","lineage":["https://openalex.org/I161515732"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mahmoud Kabalan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of St. Thomas, Saint Paul, MN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of St. Thomas, Saint Paul, MN, USA","institution_ids":["https://openalex.org/I161515732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101478645","display_name":"Pritpal Singh","orcid":"https://orcid.org/0000-0002-0384-5653"},"institutions":[{"id":"https://openalex.org/I7863295","display_name":"Villanova University","ror":"https://ror.org/02g7kd627","country_code":"US","type":"education","lineage":["https://openalex.org/I7863295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pritpal Singh","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Villanova University, Villanova, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Villanova University, Villanova, PA, USA","institution_ids":["https://openalex.org/I7863295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018076209","display_name":"Dagmar Niebur","orcid":null},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dagmar Niebur","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I72816309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054338568"],"corresponding_institution_ids":["https://openalex.org/I161515732"],"apc_list":null,"apc_paid":null,"fwci":4.6833,"has_fulltext":false,"cited_by_count":84,"citation_normalized_percentile":{"value":0.95210905,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"10","issue":"1","first_page":"772","last_page":"781"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10223","display_name":"Microgrid Control and Optimization","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10223","display_name":"Microgrid Control and Optimization","score":1.0,"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/T13183","display_name":"Islanding Detection in Power Systems","score":0.9976000189781189,"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/T12277","display_name":"Frequency Control in Power Systems","score":0.982200026512146,"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/control-theory","display_name":"Control theory (sociology)","score":0.8036946058273315},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6334113478660583},{"id":"https://openalex.org/keywords/inverter","display_name":"Inverter","score":0.6084997653961182},{"id":"https://openalex.org/keywords/voltage-droop","display_name":"Voltage droop","score":0.5991418361663818},{"id":"https://openalex.org/keywords/transient","display_name":"Transient (computer programming)","score":0.487050324678421},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4797755181789398},{"id":"https://openalex.org/keywords/time-domain","display_name":"Time domain","score":0.4728311002254486},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4571942389011383},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43997105956077576},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.27459412813186646},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.20443403720855713},{"id":"https://openalex.org/keywords/voltage-source","display_name":"Voltage source","score":0.08868786692619324}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.8036946058273315},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6334113478660583},{"id":"https://openalex.org/C11190779","wikidata":"https://www.wikidata.org/wiki/Q664575","display_name":"Inverter","level":3,"score":0.6084997653961182},{"id":"https://openalex.org/C40760162","wikidata":"https://www.wikidata.org/wiki/Q10920295","display_name":"Voltage droop","level":4,"score":0.5991418361663818},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.487050324678421},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4797755181789398},{"id":"https://openalex.org/C103824480","wikidata":"https://www.wikidata.org/wiki/Q185889","display_name":"Time domain","level":2,"score":0.4728311002254486},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4571942389011383},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43997105956077576},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.27459412813186646},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.20443403720855713},{"id":"https://openalex.org/C144655898","wikidata":"https://www.wikidata.org/wiki/Q1161128","display_name":"Voltage source","level":3,"score":0.08868786692619324},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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":1,"locations":[{"id":"doi:10.1109/tsg.2017.2752146","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2017.2752146","pdf_url":null,"source":{"id":"https://openalex.org/S59604973","display_name":"IEEE Transactions on Smart Grid","issn_l":"1949-3053","issn":["1949-3053","1949-3061"],"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 Smart Grid","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","score":0.5699999928474426,"id":"https://metadata.un.org/sdg/14"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W314648005","https://openalex.org/W1592980365","https://openalex.org/W1885074354","https://openalex.org/W1969117668","https://openalex.org/W1978770230","https://openalex.org/W1985361992","https://openalex.org/W1994959046","https://openalex.org/W2000920265","https://openalex.org/W2001965107","https://openalex.org/W2022825392","https://openalex.org/W2041178557","https://openalex.org/W2046151576","https://openalex.org/W2059172529","https://openalex.org/W2069552935","https://openalex.org/W2103608457","https://openalex.org/W2104210403","https://openalex.org/W2108326722","https://openalex.org/W2110467643","https://openalex.org/W2116846721","https://openalex.org/W2125965065","https://openalex.org/W2148156895","https://openalex.org/W2151903076","https://openalex.org/W2166911158","https://openalex.org/W2343323892","https://openalex.org/W2594908805","https://openalex.org/W4206184777","https://openalex.org/W6734944724"],"related_works":["https://openalex.org/W2523432015","https://openalex.org/W2765340260","https://openalex.org/W2153130273","https://openalex.org/W2076823813","https://openalex.org/W2143080380","https://openalex.org/W1589163333","https://openalex.org/W3008686614","https://openalex.org/W2060924671","https://openalex.org/W3180072344","https://openalex.org/W2765623668"],"abstract_inverted_index":{"The":[0,60,80,107,132],"transient":[1,24,30],"stability":[2,25,31],"of":[3,12,26,32,49,82,92,101,109,127,130,148,160,165,181,202],"inverter-based":[4],"microgrids":[5,13],"is":[6,85,112],"important":[7],"given":[8],"the":[9,29,45,68,83,88,93,99,102,125,128,137,163,166,194,200,203],"low":[10],"inertia":[11],"especially":[14],"in":[15,97],"islanded":[16],"mode.":[17],"However,":[18],"as":[19],"a":[20,50],"prerequisite":[21],"to":[22,56,66,86,135,140,175,188,199],"understanding":[23],"such":[27],"microgrids,":[28],"individual":[33],"inverters":[34],"requires":[35],"further":[36],"analysis.":[37],"To":[38],"address":[39],"inverter":[40,54],"stability,":[41],"this":[42],"paper":[43],"presents":[44],"13th-order":[46],"nonlinear":[47,69,105],"model":[48,70,111,139,169],"dc/ac":[51],"droop":[52],"controlled":[53],"connected":[55],"an":[57],"infinite":[58],"bus.":[59],"singular":[61],"perturbation":[62],"method":[63],"was":[64],"used":[65,174],"decompose":[67],"into":[71,178],"11th,":[72],"9th,":[73],"7th,":[74],"5th,":[75],"3rd,":[76],"and":[77,90,121,146,192],"1st-order":[78],"models.":[79],"aim":[81],"study":[84,204],"understand":[87],"accuracy":[89],"validity":[91],"reduced":[94,155],"order":[95,104,156,168],"models":[96,157],"replicating":[98],"performance":[100,108,164],"full":[103,167],"model.":[106],"each":[110],"investigated":[113],"using":[114],"two":[115],"different":[116],"tools,":[117],"time":[118,143],"domain":[119,129,144,147],"simulations":[120,145],"Lyapunov":[122],"functions":[123],"for":[124,142],"estimation":[126],"attraction.":[131],"work":[133],"aims":[134],"present":[136],"best":[138],"use":[141],"attraction":[149],"estimation.":[150],"Results":[151],"show":[152],"that":[153],"certain":[154],"are":[158],"capable":[159],"accurately":[161],"reproducing":[162],"while":[170],"others":[171],"can":[172],"be":[173],"gain":[176],"insights":[177],"those":[179],"areas":[180],"study.":[182],"This":[183],"will":[184],"enable":[185],"future":[186],"studies":[187],"save":[189],"computational":[190],"effort":[191],"produce":[193],"most":[195],"accurate":[196],"results":[197],"according":[198],"needs":[201],"being":[205],"performed.":[206]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":4}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}
