{"id":"https://openalex.org/W3186157838","doi":"https://doi.org/10.1109/tnse.2021.3097972","title":"Modal Decomposition of the Linear Swing Equation in Networks With Symmetries","display_name":"Modal Decomposition of the Linear Swing Equation in Networks With Symmetries","publication_year":2021,"publication_date":"2021-07-01","ids":{"openalex":"https://openalex.org/W3186157838","doi":"https://doi.org/10.1109/tnse.2021.3097972","mag":"3186157838"},"language":"en","primary_location":{"id":"doi:10.1109/tnse.2021.3097972","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2021.3097972","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"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 Network Science and Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2107.10927","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019343830","display_name":"Kshitij Bhatta","orcid":"https://orcid.org/0000-0002-7884-9667"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kshitij Bhatta","raw_affiliation_strings":["Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM, USA","institution_ids":["https://openalex.org/I169521973"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086774219","display_name":"Majeed M. Hayat","orcid":"https://orcid.org/0000-0002-3606-0406"},"institutions":[{"id":"https://openalex.org/I102461120","display_name":"Marquette University","ror":"https://ror.org/04gr4te78","country_code":"US","type":"education","lineage":["https://openalex.org/I102461120"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Majeed M. Hayat","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Marquette University, Milwakee, WI, USA"],"raw_orcid":"https://orcid.org/0000-0002-3606-0406","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Marquette University, Milwakee, WI, USA","institution_ids":["https://openalex.org/I102461120"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034065247","display_name":"Francesco Sorrentino","orcid":"https://orcid.org/0000-0001-8899-1176"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Francesco Sorrentino","raw_affiliation_strings":["Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM, USA"],"raw_orcid":"https://orcid.org/0000-0001-8899-1176","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM, USA","institution_ids":["https://openalex.org/I169521973"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2045,"currency":"USD","value_usd":2045},"apc_paid":null,"fwci":0.5689,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.62467907,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"8","issue":"3","first_page":"2482","last_page":"2494"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10305","display_name":"Power System Optimization and Stability","score":0.9975000023841858,"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":0.9975000023841858,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10917","display_name":"Smart Grid Security and Resilience","score":0.9751999974250793,"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/homogeneous-space","display_name":"Homogeneous space","score":0.7026050090789795},{"id":"https://openalex.org/keywords/swing","display_name":"Swing","score":0.5387829542160034},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48975682258605957},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4718190133571625},{"id":"https://openalex.org/keywords/transient","display_name":"Transient (computer programming)","score":0.45015662908554077},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4464016258716583},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.43451541662216187},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.43192580342292786},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3438454866409302},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34131166338920593},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.275652676820755},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07756087183952332},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07659950852394104}],"concepts":[{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.7026050090789795},{"id":"https://openalex.org/C65655974","wikidata":"https://www.wikidata.org/wiki/Q14867674","display_name":"Swing","level":2,"score":0.5387829542160034},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48975682258605957},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4718190133571625},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.45015662908554077},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4464016258716583},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.43451541662216187},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.43192580342292786},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3438454866409302},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34131166338920593},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.275652676820755},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07756087183952332},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07659950852394104},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnse.2021.3097972","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2021.3097972","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"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 Network Science and Engineering","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2107.10927","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2107.10927","pdf_url":"https://arxiv.org/pdf/2107.10927","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2107.10927","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2107.10927","pdf_url":"https://arxiv.org/pdf/2107.10927","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[],"awards":[{"id":"https://openalex.org/G2287730654","display_name":"Collaborative Research:  CRISP Type 2: Revolution through Evolution: A Controls Approach to Improve How Society Interacts with Electricity","funder_award_id":"1541148","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4725945098","display_name":"Dynamics of Coupled Heterogeneous Oscillators with Application to Biological Systems","funder_award_id":"1727948","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W10127431","https://openalex.org/W1509227760","https://openalex.org/W1512593738","https://openalex.org/W1538056276","https://openalex.org/W1967266987","https://openalex.org/W1968686485","https://openalex.org/W1999647190","https://openalex.org/W2010478496","https://openalex.org/W2025761485","https://openalex.org/W2047232486","https://openalex.org/W2057864643","https://openalex.org/W2071090652","https://openalex.org/W2073060976","https://openalex.org/W2075542919","https://openalex.org/W2078029337","https://openalex.org/W2081805716","https://openalex.org/W2083638266","https://openalex.org/W2088621938","https://openalex.org/W2097771670","https://openalex.org/W2098581246","https://openalex.org/W2106034715","https://openalex.org/W2106365068","https://openalex.org/W2108951013","https://openalex.org/W2109046263","https://openalex.org/W2110907155","https://openalex.org/W2112920805","https://openalex.org/W2118044321","https://openalex.org/W2143708085","https://openalex.org/W2145109236","https://openalex.org/W2145856299","https://openalex.org/W2147040528","https://openalex.org/W2155202145","https://openalex.org/W2158443610","https://openalex.org/W2412286290","https://openalex.org/W2510701725","https://openalex.org/W2534504831","https://openalex.org/W2739337234","https://openalex.org/W2756907874","https://openalex.org/W2769051030","https://openalex.org/W2789679217","https://openalex.org/W2793652243","https://openalex.org/W2795733431","https://openalex.org/W2799024262","https://openalex.org/W2804302282","https://openalex.org/W2896057756","https://openalex.org/W2907512112","https://openalex.org/W2963540556","https://openalex.org/W2963829782","https://openalex.org/W2964217722","https://openalex.org/W2966267214","https://openalex.org/W2989659188","https://openalex.org/W3036953780","https://openalex.org/W3039576359","https://openalex.org/W3049187163","https://openalex.org/W3099323801","https://openalex.org/W3099919647","https://openalex.org/W3104677896","https://openalex.org/W3105901970","https://openalex.org/W3145665386","https://openalex.org/W4212821273","https://openalex.org/W4238017159","https://openalex.org/W4407099190","https://openalex.org/W6642084206","https://openalex.org/W6681913206","https://openalex.org/W6766253151"],"related_works":["https://openalex.org/W2360051520","https://openalex.org/W2798244654","https://openalex.org/W3168108534","https://openalex.org/W34871393","https://openalex.org/W4206135463","https://openalex.org/W1486689224","https://openalex.org/W2094697992","https://openalex.org/W2998806118","https://openalex.org/W4229574949","https://openalex.org/W2368813785"],"abstract_inverted_index":{"Symmetries":[0],"are":[1],"widespread":[2],"in":[3,67,94,123],"physical,":[4],"technological,":[5],"biological,":[6],"and":[7,10,45,84,109],"social":[8],"systems":[9],"networks,":[11],"including":[12],"power":[13,138],"grids.":[14],"The":[15,28],"swing":[16,42],"equation":[17,43],"is":[18,34,115],"a":[19,51,86,136],"classic":[20],"model":[21,114],"for":[22],"the":[23,41,63,68,77,81,90,95,99,113],"dynamics":[24],"of":[25,31,65,89,92,107,132],"powergrid":[26],"networks.":[27],"main":[29],"goal":[30],"this":[32],"paper":[33],"to":[35,57,104,117,135],"explain":[36],"how":[37,119],"network":[38,82,96,140],"symmetries":[39,93],"affect":[40],"transient":[44,59],"steady":[46],"state":[47],"dynamics.":[48,100],"We":[49],"introduce":[50],"modal":[52,72],"decomposition":[53,73],"that":[54,141],"allows":[55,85],"us":[56],"study":[58],"effects,":[60],"such":[61],"as":[62],"presence":[64],"overshoots":[66],"system":[69],"response.":[70],"This":[71],"provides":[74],"insight":[75],"into":[76],"peak":[78],"flows":[79],"within":[80],"lines":[83],"rigorous":[87],"characterization":[88],"effects":[91],"topology":[97],"on":[98],"Our":[101],"work":[102],"applies":[103],"both":[105],"cases":[106],"homogeneous":[108],"heterogeneous":[110],"parameters.":[111],"Further,":[112],"used":[116],"show":[118],"small":[120],"perturbations":[121],"propagate":[122],"networks":[124],"with":[125],"symmetries.":[126,143],"Finally,":[127],"we":[128],"present":[129],"an":[130],"application":[131],"our":[133],"approach":[134],"large":[137],"grid":[139],"displays":[142]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}