{"id":"https://openalex.org/W2901376666","doi":"https://doi.org/10.1109/tcst.2018.2878548","title":"Load Control Problems in Direct Current Distribution Networks: Optimality, Equilibrium of Games","display_name":"Load Control Problems in Direct Current Distribution Networks: Optimality, Equilibrium of Games","publication_year":2018,"publication_date":"2018-11-13","ids":{"openalex":"https://openalex.org/W2901376666","doi":"https://doi.org/10.1109/tcst.2018.2878548","mag":"2901376666"},"language":"en","primary_location":{"id":"doi:10.1109/tcst.2018.2878548","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2018.2878548","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"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 Control Systems Technology","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/A5073256902","display_name":"Suli Zou","orcid":"https://orcid.org/0000-0003-1508-8458"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Suli Zou","raw_affiliation_strings":["National Key Laboratory of Complex System Intelligent Control and Decision, BIT, Beijing, China","School of Automation, Beijing Institute of Technology (BIT), Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-1508-8458","affiliations":[{"raw_affiliation_string":"National Key Laboratory of Complex System Intelligent Control and Decision, BIT, Beijing, China","institution_ids":[]},{"raw_affiliation_string":"School of Automation, Beijing Institute of Technology (BIT), Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035188278","display_name":"Zhongjing Ma","orcid":"https://orcid.org/0000-0002-1617-7201"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongjing Ma","raw_affiliation_strings":["National Key Laboratory of Complex System Intelligent Control and Decision, BIT, Beijing, China","School of Automation, Beijing Institute of Technology (BIT), Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-1617-7201","affiliations":[{"raw_affiliation_string":"National Key Laboratory of Complex System Intelligent Control and Decision, BIT, Beijing, China","institution_ids":[]},{"raw_affiliation_string":"School of Automation, Beijing Institute of Technology (BIT), Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100449792","display_name":"Shan Liu","orcid":"https://orcid.org/0000-0002-1846-3789"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shan Liu","raw_affiliation_strings":["National Key Laboratory of Complex System Intelligent Control and Decision, BIT, Beijing, China","School of Automation, Beijing Institute of Technology (BIT), Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Complex System Intelligent Control and Decision, BIT, Beijing, China","institution_ids":[]},{"raw_affiliation_string":"School of Automation, Beijing Institute of Technology (BIT), Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I125839683"],"apc_list":null,"apc_paid":null,"fwci":0.2525,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.57586366,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"28","issue":"2","first_page":"347","last_page":"360"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10603","display_name":"Smart Grid Energy Management","score":0.9998999834060669,"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/T10603","display_name":"Smart Grid Energy Management","score":0.9998999834060669,"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/T10454","display_name":"Optimal Power Flow Distribution","score":0.9997000098228455,"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":0.9991999864578247,"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/control","display_name":"Control (management)","score":0.6164811253547668},{"id":"https://openalex.org/keywords/current","display_name":"Current (fluid)","score":0.5183021426200867},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4513685405254364},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.434756338596344},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41864585876464844},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.41565585136413574},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3671134114265442},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.29667535424232483},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28912895917892456},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.1019008457660675},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08090990781784058}],"concepts":[{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.6164811253547668},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.5183021426200867},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4513685405254364},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.434756338596344},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41864585876464844},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.41565585136413574},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3671134114265442},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.29667535424232483},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28912895917892456},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.1019008457660675},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08090990781784058}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcst.2018.2878548","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2018.2878548","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"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 Control Systems Technology","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1448491678","display_name":null,"funder_award_id":"61873303","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W187184694","https://openalex.org/W1488435683","https://openalex.org/W1976883400","https://openalex.org/W1977464588","https://openalex.org/W1983960311","https://openalex.org/W1989357193","https://openalex.org/W1990631613","https://openalex.org/W1993873232","https://openalex.org/W2003607543","https://openalex.org/W2009610434","https://openalex.org/W2010739835","https://openalex.org/W2012022027","https://openalex.org/W2040788592","https://openalex.org/W2041684917","https://openalex.org/W2043922364","https://openalex.org/W2046252932","https://openalex.org/W2046804341","https://openalex.org/W2080108722","https://openalex.org/W2084633128","https://openalex.org/W2095508122","https://openalex.org/W2103511841","https://openalex.org/W2103790645","https://openalex.org/W2109375302","https://openalex.org/W2111369734","https://openalex.org/W2112395820","https://openalex.org/W2119405005","https://openalex.org/W2128661890","https://openalex.org/W2129129019","https://openalex.org/W2131019359","https://openalex.org/W2153117182","https://openalex.org/W2157030448","https://openalex.org/W2159014131","https://openalex.org/W2170736358","https://openalex.org/W2319782977","https://openalex.org/W2327238720","https://openalex.org/W2333242453","https://openalex.org/W2418228673","https://openalex.org/W2428788477","https://openalex.org/W2466205282","https://openalex.org/W2526316194","https://openalex.org/W3098546508","https://openalex.org/W4231143303","https://openalex.org/W4237348938","https://openalex.org/W4242705806","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W1512850994","https://openalex.org/W1990815933","https://openalex.org/W3147593538","https://openalex.org/W1491833039","https://openalex.org/W1973141406","https://openalex.org/W3129916666","https://openalex.org/W2802082827","https://openalex.org/W2793397989","https://openalex.org/W3136115002","https://openalex.org/W2030355453"],"abstract_inverted_index":{"Due":[0],"to":[1,66,93,106,108,141],"the":[2,14,22,33,49,54,58,95,102,109,113,123,129,134,142,161,168,171,177],"promising":[3],"development":[4],"of":[5,24,37,78,128,144,151,170,176],"direct":[6],"current":[7],"(dc)":[8],"distribution":[9,29,145],"networks,":[10],"we":[11,41,71,121],"focus":[12],"on":[13,32,89],"demand-side":[15],"management":[16],"(DSM)":[17],"problems":[18],"which":[19],"aim":[20],"at":[21],"minimization":[23],"operational":[25],"costs":[26],"in":[27,148,167],"dc":[28],"networks.":[30,146],"Based":[31],"established":[34],"voltage":[35,51],"model":[36],"power":[38],"electronic":[39],"loads,":[40],"formulate":[42],"a":[43,76,85],"DSM":[44],"optimization":[45,60,163],"problem":[46,61,164],"that":[47,101],"coordinates":[48],"bus":[50],"by":[52,159],"minimizing":[53],"system":[55,103],"cost,":[56],"and":[57,82,91,125,132,137,182],"underlying":[59,162],"is":[62,99,104,165,180],"nonconvex.":[63],"In":[64],"order":[65],"solve":[67],"this":[68],"nonconvex":[69],"problem,":[70,81],"first":[72],"reformulate":[73],"it":[74],"as":[75],"difference":[77],"convex":[79],"programming":[80],"then":[83],"propose":[84],"novel":[86],"algorithm":[87],"based":[88],"branch":[90],"bound":[92],"implement":[94],"optimal":[96],"solution.":[97],"It":[98],"shown":[100],"guaranteed":[105],"converge":[107],"global":[110,126],"optimum":[111],"under":[112],"proposed":[114,130],"method.":[115],"As":[116],"demonstrated":[117,183],"with":[118,139],"numerical":[119],"examples,":[120],"analyze":[122],"convergence":[124],"optimality":[127],"method,":[131],"discuss":[133],"computational":[135],"complexity":[136],"scalability":[138],"respect":[140],"size":[143],"Moreover,":[147],"case":[149],"each":[150],"individual":[152],"loads":[153],"can":[154],"make":[155],"its":[156],"own":[157],"decisions":[158],"itself,":[160],"implemented":[166],"context":[169],"noncooperative":[172],"game.":[173],"The":[174],"existence":[175],"Nash":[178],"equilibrium":[179],"verified":[181],"through":[184],"simulation":[185],"results.":[186]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}