{"id":"https://openalex.org/W2953143021","doi":"https://doi.org/10.1109/tsg.2017.2731811","title":"Distributed Frequency Control With Operational Constraints, Part II: Network Power Balance","display_name":"Distributed Frequency Control With Operational Constraints, Part II: Network Power Balance","publication_year":2017,"publication_date":"2017-07-25","ids":{"openalex":"https://openalex.org/W2953143021","doi":"https://doi.org/10.1109/tsg.2017.2731811","mag":"2953143021"},"language":"en","primary_location":{"id":"doi:10.1109/tsg.2017.2731811","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2017.2731811","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/A5053837522","display_name":"Zhaojian Wang","orcid":"https://orcid.org/0000-0002-4998-6339"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhaojian Wang","raw_affiliation_strings":["Department of Electrical Engineering, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100415332","display_name":"Feng Liu","orcid":"https://orcid.org/0000-0003-2279-2558"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng Liu","raw_affiliation_strings":["Department of Electrical Engineering, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069455858","display_name":"Steven H. Low","orcid":"https://orcid.org/0000-0001-6476-3048"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steven H. Low","raw_affiliation_strings":["Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015970180","display_name":"Changhong Zhao","orcid":"https://orcid.org/0000-0003-0539-8591"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Changhong Zhao","raw_affiliation_strings":["Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000459401","display_name":"Shengwei Mei","orcid":"https://orcid.org/0000-0002-2757-5977"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shengwei Mei","raw_affiliation_strings":["Department of Electrical Engineering, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5053837522"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":3.2969,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.92895676,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"10","issue":"1","first_page":"53","last_page":"64"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12277","display_name":"Frequency Control in Power Systems","score":0.9994999766349792,"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/T12277","display_name":"Frequency Control in Power Systems","score":0.9994999766349792,"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":0.9988999962806702,"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/T11102","display_name":"HVDC Systems and Fault Protection","score":0.9926999807357788,"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":0.8289350271224976},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.6514587998390198},{"id":"https://openalex.org/keywords/automatic-frequency-control","display_name":"Automatic frequency control","score":0.6220470666885376},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5848152041435242},{"id":"https://openalex.org/keywords/power-balance","display_name":"Power Balance","score":0.5481144189834595},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.5020053386688232},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.4728429913520813},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4546218514442444},{"id":"https://openalex.org/keywords/tie-line","display_name":"Tie line","score":0.45143893361091614},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.43589940667152405},{"id":"https://openalex.org/keywords/transient","display_name":"Transient (computer programming)","score":0.4248824119567871},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41208162903785706},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3513786792755127},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.3476753234863281},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.339588463306427},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.30937957763671875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24452540278434753},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.08306008577346802}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.8289350271224976},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.6514587998390198},{"id":"https://openalex.org/C25915539","wikidata":"https://www.wikidata.org/wiki/Q220786","display_name":"Automatic frequency control","level":2,"score":0.6220470666885376},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5848152041435242},{"id":"https://openalex.org/C2780848588","wikidata":"https://www.wikidata.org/wiki/Q210494","display_name":"Power Balance","level":3,"score":0.5481144189834595},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.5020053386688232},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4728429913520813},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4546218514442444},{"id":"https://openalex.org/C32866971","wikidata":"https://www.wikidata.org/wiki/Q7800957","display_name":"Tie line","level":4,"score":0.45143893361091614},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.43589940667152405},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.4248824119567871},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41208162903785706},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3513786792755127},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3476753234863281},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.339588463306427},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.30937957763671875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24452540278434753},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.08306008577346802},{"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/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsg.2017.2731811","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2017.2731811","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"},{"id":"pmh:oai:authors.library.caltech.edu:79458","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20170726-155035857","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5899999737739563,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G1788142325","display_name":null,"funder_award_id":"EPCN 1619352","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1944249978","display_name":null,"funder_award_id":"51621065","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2013955184","display_name":null,"funder_award_id":"51677100","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4096073654","display_name":null,"funder_award_id":"CCF 1637598","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5829475755","display_name":null,"funder_award_id":"51377092","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6748038075","display_name":null,"funder_award_id":"DE-AR0000699","funder_id":"https://openalex.org/F4320332276","funder_display_name":"Advanced Research Projects Agency - Energy"},{"id":"https://openalex.org/G8732195525","display_name":null,"funder_award_id":"CNS 1545096","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"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320332276","display_name":"Advanced Research Projects Agency - Energy","ror":"https://ror.org/03q1rgc19"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1551360398","https://openalex.org/W1664854972","https://openalex.org/W1763243278","https://openalex.org/W1795440635","https://openalex.org/W1858766554","https://openalex.org/W1975847594","https://openalex.org/W1985348591","https://openalex.org/W1997958693","https://openalex.org/W2006114567","https://openalex.org/W2022513306","https://openalex.org/W2038275162","https://openalex.org/W2051287288","https://openalex.org/W2065322876","https://openalex.org/W2086929129","https://openalex.org/W2102739878","https://openalex.org/W2117618281","https://openalex.org/W2143776086","https://openalex.org/W2154414031","https://openalex.org/W2207156949","https://openalex.org/W2215067230","https://openalex.org/W2224468021","https://openalex.org/W2292494108","https://openalex.org/W2304026854","https://openalex.org/W2339703115","https://openalex.org/W2508693252","https://openalex.org/W2520314131","https://openalex.org/W2567786659","https://openalex.org/W2623904884","https://openalex.org/W2953143021","https://openalex.org/W2963135216","https://openalex.org/W2963246511","https://openalex.org/W2963686095","https://openalex.org/W3016074254"],"related_works":["https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W2954898248","https://openalex.org/W2050693590","https://openalex.org/W2384708701","https://openalex.org/W2090419309","https://openalex.org/W2614730187","https://openalex.org/W3096409761","https://openalex.org/W2069577804"],"abstract_inverted_index":{"In":[0,40],"Part":[1,41],"I":[2],"of":[3,13,43,126,152],"this":[4,44],"paper,":[5,45],"we":[6,46,130],"propose":[7,47],"a":[8,48],"decentralized":[9],"optimal":[10,52],"frequency":[11,53],"control":[12,38,54],"multi-area":[14],"power":[15,32,58,63],"system":[16,104],"with":[17,105,113,123],"operational":[18],"constraints,":[19],"where":[20,61],"the":[21,27,31,56,62,68,72,75,80,86,102,106,127,132,150],"tie-line":[22,76],"powers":[23,77],"remain":[24,78],"unchanged":[25],"in":[26,55],"steady":[28],"state":[29],"and":[30,95],"mismatch":[33,64],"is":[34,65,99],"balanced":[35,66],"within":[36,79],"individual":[37],"areas.":[39],"II":[42],"distributed":[49],"controller":[50,108],"for":[51,115,135],"network":[57],"balance":[59],"case,":[60],"over":[67],"whole":[69],"system.":[70],"With":[71],"proposed":[73,107],"controller,":[74],"acceptable":[81],"range":[82],"at":[83,93],"equilibrium,":[84],"while":[85],"regulation":[87],"capacity":[88],"constraints":[89],"are":[90,146],"satisfied":[91],"both":[92],"equilibrium":[94],"during":[96],"transient.":[97],"It":[98],"revealed":[100],"that":[101],"closed-loop":[103,128],"carries":[109],"out":[110],"primal-dual":[111],"updates":[112],"saturation":[114],"solving":[116],"an":[117],"associated":[118],"optimization":[119],"problem.":[120],"To":[121],"cope":[122],"discontinuous":[124],"dynamics":[125],"system,":[129],"deploy":[131],"invariance":[133],"principle":[134],"nonpathological":[136],"Lyapunov":[137],"function":[138],"to":[139,148],"prove":[140],"its":[141],"asymptotic":[142],"stability.":[143],"Simulation":[144],"results":[145],"provided":[147],"show":[149],"effectiveness":[151],"our":[153],"controller.":[154]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
