{"id":"https://openalex.org/W4390576202","doi":"https://doi.org/10.1109/tase.2023.3347754","title":"Multiplayer Stackelberg Game-Based Intelligent Frequency Control of Power System With Line Loss Uncertainty","display_name":"Multiplayer Stackelberg Game-Based Intelligent Frequency Control of Power System With Line Loss Uncertainty","publication_year":2024,"publication_date":"2024-01-04","ids":{"openalex":"https://openalex.org/W4390576202","doi":"https://doi.org/10.1109/tase.2023.3347754"},"language":"en","primary_location":{"id":"doi:10.1109/tase.2023.3347754","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2023.3347754","pdf_url":null,"source":{"id":"https://openalex.org/S34881539","display_name":"IEEE Transactions on Automation Science and Engineering","issn_l":"1545-5955","issn":["1545-5955","1558-3783"],"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 Automation Science and Engineering","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/A5103267184","display_name":"Xin Tong","orcid":"https://orcid.org/0000-0002-7914-1847"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Tong","raw_affiliation_strings":["College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","College of Information Science and Engineering, Northeastern University, Shenyang, China"],"raw_orcid":"https://orcid.org/0000-0002-7914-1847","affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"College of Information Science and Engineering, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001225543","display_name":"Dazhong Ma","orcid":"https://orcid.org/0000-0001-9647-3694"},"institutions":[{"id":"https://openalex.org/I4391767858","display_name":"State Key Laboratory of Synthetical Automation for Process Industries","ror":"https://ror.org/0380ng272","country_code":null,"type":"facility","lineage":["https://openalex.org/I4391767858","https://openalex.org/I9224756"]},{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dazhong Ma","raw_affiliation_strings":["State Key Laboratory of Synthetical Automation for Process Industries and the College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","State Key Laboratory of Synthetical Automation for Process Industries and the College of Information Science and Engineering, Northeastern University, Shenyang, China"],"raw_orcid":"https://orcid.org/0000-0001-9647-3694","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Synthetical Automation for Process Industries and the College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","institution_ids":["https://openalex.org/I9224756","https://openalex.org/I4391767858"]},{"raw_affiliation_string":"State Key Laboratory of Synthetical Automation for Process Industries and the College of Information Science and Engineering, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756","https://openalex.org/I4391767858"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005518384","display_name":"Rui Wang","orcid":"https://orcid.org/0000-0002-6298-0716"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Wang","raw_affiliation_strings":["College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","College of Information Science and Engineering, Northeastern University, Shenyang, China"],"raw_orcid":"https://orcid.org/0000-0002-6298-0716","affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"College of Information Science and Engineering, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021659366","display_name":"Qiuye Sun","orcid":"https://orcid.org/0000-0001-8801-0884"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiuye Sun","raw_affiliation_strings":["College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","College of Information Science and Engineering, Northeastern University, Shenyang, China"],"raw_orcid":"https://orcid.org/0000-0001-8801-0884","affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"College of Information Science and Engineering, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100625792","display_name":"Huaguang Zhang","orcid":"https://orcid.org/0000-0002-2375-9824"},"institutions":[{"id":"https://openalex.org/I4391767858","display_name":"State Key Laboratory of Synthetical Automation for Process Industries","ror":"https://ror.org/0380ng272","country_code":null,"type":"facility","lineage":["https://openalex.org/I4391767858","https://openalex.org/I9224756"]},{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huaguang Zhang","raw_affiliation_strings":["State Key Laboratory of Synthetical Automation for Process Industries and the College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","State Key Laboratory of Synthetical Automation for Process Industries and the College of Information Science and Engineering, Northeastern University, Shenyang, China"],"raw_orcid":"https://orcid.org/0000-0002-2375-9824","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Synthetical Automation for Process Industries and the College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China","institution_ids":["https://openalex.org/I9224756","https://openalex.org/I4391767858"]},{"raw_affiliation_string":"State Key Laboratory of Synthetical Automation for Process Industries and the College of Information Science and Engineering, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756","https://openalex.org/I4391767858"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6292,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.8211131,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"22","issue":null,"first_page":"154","last_page":"167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10223","display_name":"Microgrid Control and Optimization","score":0.9905999898910522,"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":0.9905999898910522,"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/T12277","display_name":"Frequency Control in Power Systems","score":0.9890000224113464,"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":0.9751999974250793,"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/stackelberg-competition","display_name":"Stackelberg competition","score":0.8429101705551147},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6989156007766724},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.581167995929718},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5160255432128906},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5055432319641113},{"id":"https://openalex.org/keywords/automatic-frequency-control","display_name":"Automatic frequency control","score":0.499417781829834},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.4864954352378845},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.4604310393333435},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.43324604630470276},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4303893446922302},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.26012855768203735},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.2475336790084839},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.15937089920043945},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11357611417770386}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.8429101705551147},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6989156007766724},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.581167995929718},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5160255432128906},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5055432319641113},{"id":"https://openalex.org/C25915539","wikidata":"https://www.wikidata.org/wiki/Q220786","display_name":"Automatic frequency control","level":2,"score":0.499417781829834},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.4864954352378845},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.4604310393333435},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.43324604630470276},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4303893446922302},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.26012855768203735},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2475336790084839},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.15937089920043945},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11357611417770386},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tase.2023.3347754","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2023.3347754","pdf_url":null,"source":{"id":"https://openalex.org/S34881539","display_name":"IEEE Transactions on Automation Science and Engineering","issn_l":"1545-5955","issn":["1545-5955","1558-3783"],"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 Automation Science and Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G192486371","display_name":null,"funder_award_id":"U22A20221","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G451589156","display_name":null,"funder_award_id":"2018YFA0702200","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G8644478913","display_name":null,"funder_award_id":"62073064","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8701110942","display_name":null,"funder_award_id":"2022-KF-11-02","funder_id":"https://openalex.org/F4320323086","funder_display_name":"Natural Science Foundation of Liaoning Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323086","display_name":"Natural Science Foundation of Liaoning Province","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1968908471","https://openalex.org/W2027270344","https://openalex.org/W2046432675","https://openalex.org/W2071780137","https://openalex.org/W2122032342","https://openalex.org/W2165182598","https://openalex.org/W2249513906","https://openalex.org/W2291165559","https://openalex.org/W2326904463","https://openalex.org/W2465923267","https://openalex.org/W2515863312","https://openalex.org/W2606262161","https://openalex.org/W2626202112","https://openalex.org/W2804243741","https://openalex.org/W2807860438","https://openalex.org/W2899431647","https://openalex.org/W2904794775","https://openalex.org/W2915707381","https://openalex.org/W2945728374","https://openalex.org/W2969168777","https://openalex.org/W2997630774","https://openalex.org/W3011048250","https://openalex.org/W3032958247","https://openalex.org/W3035460113","https://openalex.org/W3035740474","https://openalex.org/W3045788884","https://openalex.org/W3082302667","https://openalex.org/W3117972370","https://openalex.org/W3135756020","https://openalex.org/W3193760608","https://openalex.org/W3208226475","https://openalex.org/W3212986819","https://openalex.org/W4206055555","https://openalex.org/W4248917300","https://openalex.org/W4285248835","https://openalex.org/W4285505818","https://openalex.org/W4312379512","https://openalex.org/W4313449759","https://openalex.org/W4313892934","https://openalex.org/W4319990437","https://openalex.org/W6754148645"],"related_works":["https://openalex.org/W1987562536","https://openalex.org/W4383533535","https://openalex.org/W2375814310","https://openalex.org/W4380353856","https://openalex.org/W2347216446","https://openalex.org/W1995212308","https://openalex.org/W2733656312","https://openalex.org/W2976114880","https://openalex.org/W2328458106","https://openalex.org/W3092774214"],"abstract_inverted_index":{"The":[0,84,265],"power":[1,39,198],"fluctuation":[2],"and":[3,18,48,77,90,135,192,220,279,290,306],"system":[4,40,203,213,276,289],"inertia":[5],"degradation":[6],"in":[7,194,207,234,240],"a":[8,128],"short":[9],"time":[10],"put":[11],"forward":[12],"higher":[13],"requirements":[14],"on":[15,67,261],"the":[16,42,71,75,82,96,101,104,118,122,143,149,162,166,179,182,208,212,245,262,273,284,288,300],"rapidity":[17],"robustness":[19,193],"of":[20,37,44,60,88,103,121,148,168,181,197,211,287],"frequency":[21,35,54,195,215,250,257],"control.":[22],"This":[23,252],"paper":[24,253],"proposes":[25,254],"an":[26,52,109,255],"online":[27,125,282],"multiplayer":[28],"Stackelberg":[29,68,263],"game":[30],"control":[31,36,55,123,196,216,224,235,258,277],"framework":[32],"to":[33,116,160,188,243,249,271,294],"achieve":[34],"multi-area":[38],"with":[41,100,131,291],"uncertainties":[43],"load,":[45],"renewable":[46],"energy":[47],"line":[49,136,241],"loss.":[50],"Firstly,":[51],"optimal":[53,163],"model":[56],"incorporating":[57],"efficient":[58],"management":[59],"load":[61],"aggregators":[62],"(LA)":[63],"is":[64,92,114,158,172,200,269,307],"designed":[65,115,266],"based":[66,260],"game,":[69],"where":[70],"LA":[72],"acts":[73],"as":[74,81],"leader":[76,89],"all":[78,139],"micro-turbines":[79],"act":[80],"followers.":[83],"two-level":[85],"optimization":[86],"problem":[87],"followers":[91],"converted":[93],"into":[94],"solving":[95],"coupled":[97],"Hamilton-Jacobi":[98],"equations":[99],"constraints":[102],"follower\u2019s":[105],"costate":[106],"equation.":[107],"Then,":[108],"improved":[110],"integral":[111],"reinforcement":[112],"learning":[113],"enhance":[117],"wide":[119,292],"adaptability":[120,293],"strategy":[124],"by":[126],"introducing":[127],"general":[129],"function":[130],"uncertainty":[132],"upper":[133],"bounds":[134],"losses":[137,242],"for":[138,202],"players,":[140],"while":[141,232],"satisfying":[142],"uniform":[144],"ultimate":[145],"bounded":[146],"stability":[147],"closed-loop":[150],"system.":[151],"A":[152],"single":[153],"critic":[154],"neural":[155,169],"network":[156,170],"structure":[157],"utilized":[159],"obtain":[161],"strategy.":[164],"And":[165],"convergence":[167],"weights":[171],"proven.":[173],"Last,":[174],"comparative":[175],"simulation":[176],"results":[177,297],"verify":[178],"effectiveness":[180],"proposed":[183,301],"method.":[184],"<italic":[185],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[186],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Note":[187],"Practitioners</i>":[189],"\u2014High":[190],"accuracy":[191],"systems":[199],"important":[201],"safety.":[204],"Demand-side":[205],"participation":[206],"interactive":[209],"regulation":[210],"makes":[214],"strategies":[217,305],"more":[218],"flexible":[219],"diversified.":[221],"However,":[222],"unreasonable":[223],"allocation":[225],"schemes":[226],"can":[227,236],"incur":[228],"large":[229],"payment":[230,280],"costs,":[231],"changes":[233,239],"cause":[237],"dynamic":[238],"affect":[244],"supply-demand":[246],"balance,":[247],"leading":[248],"deviations.":[251],"intelligent":[256],"method":[259,302],"game.":[264],"IRL":[267],"algorithm":[268],"able":[270],"solve":[272],"trade-off":[274],"between":[275],"performance":[278],"costs":[281],"without":[283],"priori":[285],"knowledge":[286],"uncertainty.":[295],"Simulation":[296],"show":[298],"that":[299],"outperforms":[303],"non-game":[304],"robust.":[308]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}