{"id":"https://openalex.org/W4415821040","doi":"https://doi.org/10.1109/tii.2025.3620383","title":"Nash Equilibrium Among Mobile Energy Storage Systems Game for Load Restoration of Faulted Microgrids","display_name":"Nash Equilibrium Among Mobile Energy Storage Systems Game for Load Restoration of Faulted Microgrids","publication_year":2025,"publication_date":"2025-11-03","ids":{"openalex":"https://openalex.org/W4415821040","doi":"https://doi.org/10.1109/tii.2025.3620383"},"language":null,"primary_location":{"id":"doi:10.1109/tii.2025.3620383","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tii.2025.3620383","pdf_url":null,"source":{"id":"https://openalex.org/S184777250","display_name":"IEEE Transactions on Industrial Informatics","issn_l":"1551-3203","issn":["1551-3203","1941-0050"],"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 Industrial Informatics","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/A5038241786","display_name":"Yue Zhang","orcid":"https://orcid.org/0000-0001-9571-2059"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yue Zhang","raw_affiliation_strings":["Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031887275","display_name":"Xiao\u2010Kang Liu","orcid":"https://orcid.org/0000-0001-6262-6779"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao-Kang Liu","raw_affiliation_strings":["Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010845083","display_name":"Yuanzheng Li","orcid":"https://orcid.org/0000-0001-8052-1233"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanzheng Li","raw_affiliation_strings":["Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090447443","display_name":"Yan\u2010Wu Wang","orcid":"https://orcid.org/0000-0002-4722-1332"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan-Wu Wang","raw_affiliation_strings":["Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035300094","display_name":"Pierluigi Siano","orcid":"https://orcid.org/0000-0002-0975-0241"},"institutions":[{"id":"https://openalex.org/I131729948","display_name":"University of Salerno","ror":"https://ror.org/0192m2k53","country_code":"IT","type":"education","lineage":["https://openalex.org/I131729948"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Pierluigi Siano","raw_affiliation_strings":["Department of Management &amp; Innovation Systems, University of Salerno, Fisciano, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Management &amp; Innovation Systems, University of Salerno, Fisciano, Italy","institution_ids":["https://openalex.org/I131729948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5038241786"],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.43102351,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"2","first_page":"1016","last_page":"1027"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10223","display_name":"Microgrid Control and Optimization","score":0.7620000243186951,"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":0.7620000243186951,"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/T10603","display_name":"Smart Grid Energy Management","score":0.19220000505447388,"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/T11392","display_name":"Energy Harvesting in Wireless Networks","score":0.006399999838322401,"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/nash-equilibrium","display_name":"Nash equilibrium","score":0.7958999872207642},{"id":"https://openalex.org/keywords/energy-storage","display_name":"Energy storage","score":0.572700023651123},{"id":"https://openalex.org/keywords/price-of-anarchy","display_name":"Price of anarchy","score":0.564300000667572},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.546500027179718},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.43209999799728394},{"id":"https://openalex.org/keywords/price-of-stability","display_name":"Price of stability","score":0.4113999903202057},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.3910999894142151},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.36579999327659607},{"id":"https://openalex.org/keywords/battery","display_name":"Battery (electricity)","score":0.3626999855041504}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7958999872207642},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5938000082969666},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5893999934196472},{"id":"https://openalex.org/C73916439","wikidata":"https://www.wikidata.org/wiki/Q837718","display_name":"Energy storage","level":3,"score":0.572700023651123},{"id":"https://openalex.org/C82149807","wikidata":"https://www.wikidata.org/wiki/Q7242623","display_name":"Price of anarchy","level":4,"score":0.564300000667572},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.546500027179718},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.43209999799728394},{"id":"https://openalex.org/C188466206","wikidata":"https://www.wikidata.org/wiki/Q7242626","display_name":"Price of stability","level":3,"score":0.4113999903202057},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.3910999894142151},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.36910000443458557},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.36579999327659607},{"id":"https://openalex.org/C555008776","wikidata":"https://www.wikidata.org/wiki/Q267298","display_name":"Battery (electricity)","level":3,"score":0.3626999855041504},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.35519999265670776},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.3531000018119812},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.35190001130104065},{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.3391000032424927},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3357999920845032},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.3345000147819519},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3239000141620636},{"id":"https://openalex.org/C2777644927","wikidata":"https://www.wikidata.org/wiki/Q2300947","display_name":"Social cost","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.29989999532699585},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.2906999886035919},{"id":"https://openalex.org/C95491727","wikidata":"https://www.wikidata.org/wiki/Q992968","display_name":"Mobile telephony","level":3,"score":0.2863999903202057},{"id":"https://openalex.org/C2779370713","wikidata":"https://www.wikidata.org/wiki/Q357554","display_name":"Load management","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C2779438525","wikidata":"https://www.wikidata.org/wiki/Q5255048","display_name":"Demand response","level":3,"score":0.2773999869823456},{"id":"https://openalex.org/C10558101","wikidata":"https://www.wikidata.org/wiki/Q689855","display_name":"Smart grid","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.25760000944137573},{"id":"https://openalex.org/C2983254600","wikidata":"https://www.wikidata.org/wiki/Q1096907","display_name":"Power grid","level":3,"score":0.2540000081062317},{"id":"https://openalex.org/C2780165032","wikidata":"https://www.wikidata.org/wiki/Q16869822","display_name":"Energy consumption","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tii.2025.3620383","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tii.2025.3620383","pdf_url":null,"source":{"id":"https://openalex.org/S184777250","display_name":"IEEE Transactions on Industrial Informatics","issn_l":"1551-3203","issn":["1551-3203","1941-0050"],"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 Industrial Informatics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1985823893","https://openalex.org/W2023548600","https://openalex.org/W2034194462","https://openalex.org/W2145633829","https://openalex.org/W2148042342","https://openalex.org/W2531787101","https://openalex.org/W2945690175","https://openalex.org/W3022321359","https://openalex.org/W3046840235","https://openalex.org/W3175093674","https://openalex.org/W3189867955","https://openalex.org/W3205364134","https://openalex.org/W3215999434","https://openalex.org/W4220891000","https://openalex.org/W4243522648","https://openalex.org/W4285904154","https://openalex.org/W4312806588","https://openalex.org/W4319869616","https://openalex.org/W4320176130","https://openalex.org/W4321487960","https://openalex.org/W4367663222","https://openalex.org/W4378421989","https://openalex.org/W4386524000","https://openalex.org/W4388320590","https://openalex.org/W4397001005","https://openalex.org/W4398788530","https://openalex.org/W4400399897","https://openalex.org/W4403122900","https://openalex.org/W4405488561","https://openalex.org/W4408030055"],"related_works":[],"abstract_inverted_index":{"Mobile":[0],"energy":[1],"storage":[2],"systems":[3],"(MESSs)":[4],"represent":[5],"a":[6,55,70,83,88],"proactive":[7],"approach":[8],"to":[9,30,37,49,73,82,104],"load":[10,168],"restoration":[11,169],"of":[12,24,79,95],"faulted":[13],"microgrids.":[14],"Existing":[15],"studies":[16],"mainly":[17],"focus":[18],"on":[19,92],"minimizing":[20],"the":[21,25,39,62,76,93,102,113,157],"overall":[22,114],"cost":[23,42],"MESS":[26,140,161],"fleet":[27,141],"but":[28],"fail":[29],"guarantee":[31],"that":[32,75,99,137],"self-interested":[33,106],"MESSs":[34,48,80,101,176],"are":[35,149],"willing":[36],"follow":[38],"optimal":[40],"social":[41,115],"solution.":[43],"Hence,":[44],"this":[45],"article":[46],"allows":[47],"make":[50,105],"independent":[51],"decisions":[52,108],"and":[53,68,131,143,180],"formulates":[54],"nonconvex":[56],"game.":[57],"In":[58],"particular,":[59],"we":[60,118],"incorporate":[61],"maximum":[63],"tolerable":[64],"service":[65],"waiting":[66],"time":[67],"construct":[69],"potential":[71],"function":[72],"prove":[74],"selfish":[77],"actions":[78],"converge":[81],"Nash":[84,107,147],"equilibrium.":[85],"We":[86],"derive":[87],"small":[89],"upper":[90],"bound":[91],"price":[94],"anarchy":[96],"(PoA),":[97],"demonstrating":[98],"granting":[100],"autonomy":[103],"does":[109],"not":[110],"significantly":[111],"increase":[112],"cost.":[116],"Moreover,":[117],"model":[119],"subjective":[120],"behaviors":[121],"under":[122],"uncertain":[123,172],"grid":[124],"power":[125],"availability,":[126],"accounting":[127],"for":[128,138],"both":[129],"loss-sensitive":[130],"gain-seeking":[132,175],"tendencies.":[133],"Simulation":[134],"results":[135],"show":[136],"different":[139],"sizes":[142],"battery":[144,164],"anxiety":[145,165],"extents,":[146],"equilibria":[148],"always":[150],"achieved,":[151],"with":[152],"all":[153],"PoA":[154],"values":[155],"below":[156],"theoretical":[158],"bound.":[159],"Higher":[160],"numbers":[162],"or":[163],"extents":[166],"improve":[167],"performance.":[170],"Under":[171],"surplus":[173],"energy,":[174],"behave":[177],"more":[178],"aggressively":[179],"earn":[181],"higher":[182],"average":[183],"profits.":[184]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-11-03T00:00:00"}
