{"id":"https://openalex.org/W2958202502","doi":"https://doi.org/10.1109/tac.2021.3053552","title":"Transient Stability of Droop-Controlled Inverter Networks With Operating Constraints","display_name":"Transient Stability of Droop-Controlled Inverter Networks With Operating Constraints","publication_year":2021,"publication_date":"2021-01-25","ids":{"openalex":"https://openalex.org/W2958202502","doi":"https://doi.org/10.1109/tac.2021.3053552","mag":"2958202502"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3053552","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3053552","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1907.05532","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077158504","display_name":"Kevin Smith","orcid":"https://orcid.org/0000-0002-1407-5893"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kevin D. Smith","raw_affiliation_strings":["Center of Control, Dynamical Systems, and Computation, University of California Santa Barbara, Santa Barbara, CA, USA","University of California Santa Barbara"],"affiliations":[{"raw_affiliation_string":"Center of Control, Dynamical Systems, and Computation, University of California Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"University of California Santa Barbara","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014088551","display_name":"Saber Jafarpour","orcid":"https://orcid.org/0000-0002-7614-2940"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Saber Jafarpour","raw_affiliation_strings":["Center of Control, Dynamical Systems, and Computation, University of California Santa Barbara, Santa Barbara, CA, USA","University of California Santa Barbara"],"affiliations":[{"raw_affiliation_string":"Center of Control, Dynamical Systems, and Computation, University of California Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"University of California Santa Barbara","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068353454","display_name":"Francesco Bullo","orcid":"https://orcid.org/0000-0002-4785-2118"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Francesco Bullo","raw_affiliation_strings":["Center of Control, Dynamical Systems, and Computation, University of California Santa Barbara, Santa Barbara, CA, USA","University of California Santa Barbara"],"affiliations":[{"raw_affiliation_string":"Center of Control, Dynamical Systems, and Computation, University of California Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"University of California Santa Barbara","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077158504"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":0.1386,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.40030154,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"67","issue":"2","first_page":"633","last_page":"645"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10223","display_name":"Microgrid Control and Optimization","score":0.9998000264167786,"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":0.9998000264167786,"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/T10454","display_name":"Optimal Power Flow Distribution","score":0.9950000047683716,"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/T10305","display_name":"Power System Optimization and Stability","score":0.9940999746322632,"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/voltage-droop","display_name":"Voltage droop","score":0.9419134855270386},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7974108457565308},{"id":"https://openalex.org/keywords/transient","display_name":"Transient (computer programming)","score":0.7532981038093567},{"id":"https://openalex.org/keywords/inverter","display_name":"Inverter","score":0.6223737001419067},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5340598821640015},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5331752896308899},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.5251193642616272},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5113048553466797},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.47621187567710876},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.47597306966781616},{"id":"https://openalex.org/keywords/automatic-frequency-control","display_name":"Automatic frequency control","score":0.45612847805023193},{"id":"https://openalex.org/keywords/fault","display_name":"Fault (geology)","score":0.43987634778022766},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.43628358840942383},{"id":"https://openalex.org/keywords/ac-power","display_name":"AC power","score":0.428028404712677},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.3392764925956726},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.3299139738082886},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3144354820251465},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16342014074325562},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.1352258324623108},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.09578010439872742},{"id":"https://openalex.org/keywords/voltage-regulator","display_name":"Voltage regulator","score":0.08100917935371399}],"concepts":[{"id":"https://openalex.org/C40760162","wikidata":"https://www.wikidata.org/wiki/Q10920295","display_name":"Voltage droop","level":4,"score":0.9419134855270386},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7974108457565308},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.7532981038093567},{"id":"https://openalex.org/C11190779","wikidata":"https://www.wikidata.org/wiki/Q664575","display_name":"Inverter","level":3,"score":0.6223737001419067},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5340598821640015},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5331752896308899},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.5251193642616272},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5113048553466797},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.47621187567710876},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.47597306966781616},{"id":"https://openalex.org/C25915539","wikidata":"https://www.wikidata.org/wiki/Q220786","display_name":"Automatic frequency control","level":2,"score":0.45612847805023193},{"id":"https://openalex.org/C175551986","wikidata":"https://www.wikidata.org/wiki/Q47089","display_name":"Fault (geology)","level":2,"score":0.43987634778022766},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.43628358840942383},{"id":"https://openalex.org/C108755667","wikidata":"https://www.wikidata.org/wiki/Q1930258","display_name":"AC power","level":3,"score":0.428028404712677},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3392764925956726},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3299139738082886},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3144354820251465},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16342014074325562},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.1352258324623108},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.09578010439872742},{"id":"https://openalex.org/C110706871","wikidata":"https://www.wikidata.org/wiki/Q851210","display_name":"Voltage regulator","level":3,"score":0.08100917935371399},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C165205528","wikidata":"https://www.wikidata.org/wiki/Q83371","display_name":"Seismology","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tac.2021.3053552","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3053552","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1907.05532","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.05532","pdf_url":"https://arxiv.org/pdf/1907.05532","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":"mag:2958202502","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1907.05532","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1907.05532","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1907.05532","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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1907.05532","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.05532","pdf_url":"https://arxiv.org/pdf/1907.05532","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"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8999999761581421}],"awards":[{"id":"https://openalex.org/G4093260172","display_name":null,"funder_award_id":"HDTRA1-19-1-0017","funder_id":"https://openalex.org/F4320332186","funder_display_name":"Defense Threat Reduction Agency"},{"id":"https://openalex.org/G5731958760","display_name":null,"funder_award_id":"DGE-1\u00a0258\u00a0507","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"},{"id":"https://openalex.org/G8355874910","display_name":null,"funder_award_id":"DE-EE0000-1583","funder_id":"https://openalex.org/F4320337712","funder_display_name":"Solar Energy Technologies Office"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332186","display_name":"Defense Threat Reduction Agency","ror":"https://ror.org/04tz64554"},{"id":"https://openalex.org/F4320335353","display_name":"National Science Foundation of Sri Lanka","ror":"https://ror.org/010xaa060"},{"id":"https://openalex.org/F4320337712","display_name":"Solar Energy Technologies Office","ror":"https://ror.org/033jmdj81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1504052325","https://openalex.org/W1509227760","https://openalex.org/W1763243278","https://openalex.org/W1965897919","https://openalex.org/W1985821177","https://openalex.org/W1990833963","https://openalex.org/W2001647331","https://openalex.org/W2033225140","https://openalex.org/W2035144082","https://openalex.org/W2043883312","https://openalex.org/W2070221925","https://openalex.org/W2071358184","https://openalex.org/W2075514521","https://openalex.org/W2091567533","https://openalex.org/W2120747200","https://openalex.org/W2132434872","https://openalex.org/W2144716010","https://openalex.org/W2147246923","https://openalex.org/W2162156389","https://openalex.org/W2169820422","https://openalex.org/W2790571338","https://openalex.org/W2790662552","https://openalex.org/W2799657821","https://openalex.org/W2963714928","https://openalex.org/W2973150236","https://openalex.org/W2973151898","https://openalex.org/W2990566680","https://openalex.org/W3101582476","https://openalex.org/W3106066853"],"related_works":["https://openalex.org/W2791039351","https://openalex.org/W2897935695","https://openalex.org/W2025019995","https://openalex.org/W2249714677","https://openalex.org/W2562872838","https://openalex.org/W3013547907","https://openalex.org/W3156867250","https://openalex.org/W2977214025","https://openalex.org/W3046197083","https://openalex.org/W2939075464","https://openalex.org/W2924541012","https://openalex.org/W2581975284","https://openalex.org/W3175660447","https://openalex.org/W3176803657","https://openalex.org/W3200672043","https://openalex.org/W3128275982","https://openalex.org/W3096951893","https://openalex.org/W3095502181","https://openalex.org/W2987447721","https://openalex.org/W2972365224"],"abstract_inverted_index":{"Due":[0],"to":[1,55,76,92,120,127],"the":[2,8,21,33,113,122,129,142],"rise":[3],"of":[4,10,12,38,69,107,124,141],"distributed":[5],"energy":[6],"resources,":[7],"control":[9,26,30,37],"networks":[11,51],"grid-forming":[13],"inverters":[14],"is":[15,27,131],"now":[16],"a":[17,28,60,79],"pressing":[18],"issue":[19],"for":[20,35],"power":[22,109],"system":[23],"operation.":[24],"Droop":[25],"popular":[29],"strategy":[31],"in":[32,48,112],"literature":[34],"frequency":[36,83],"these":[39,118],"inverters.":[40],"In":[41],"this":[42],"article,":[43],"we":[44,65,116],"analyze":[45],"transient":[46,95],"stability":[47,96],"droop-controlled":[49],"inverter":[50],"that":[52,78],"are":[53],"subject":[54],"multiple":[56],"operating":[57,87],"constraints.":[58,88],"Using":[59],"physically":[61],"meaningful":[62],"Lyapunov-like":[63],"function,":[64],"provide":[66],"two":[67],"sets":[68],"criteria":[70],"(one":[71],"mathematical":[72],"and":[73],"one":[74],"computational)":[75],"certify":[77],"postfault":[80],"trajectory":[81],"achieves":[82],"synchronization":[84],"while":[85],"respecting":[86],"We":[89,133],"show":[90],"how":[91],"obtain":[93],"less-conservative":[94],"conditions":[97,119],"by":[98],"incorporating":[99],"information":[100],"from":[101],"loop":[102],"flows,":[103],"i.e.,":[104],"net":[105],"flows":[106],"active":[108],"around":[110],"cycles":[111],"network.":[114],"Finally,":[115],"use":[117],"quantify":[121],"scale":[123],"parameter":[125],"disturbances":[126],"which":[128],"network":[130],"robust.":[132],"illustrate":[134],"our":[135],"results":[136],"with":[137],"numerical":[138],"case":[139],"studies":[140],"IEEE":[143],"24-bus":[144],"system.":[145]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2022-07-28T00:00:00"}