{"id":"https://openalex.org/W4412567147","doi":"https://doi.org/10.1109/access.2025.3591459","title":"Two-Stage Robust Optimization Considering the Uncertainty of Sources and Loads in Virtual Power Plants","display_name":"Two-Stage Robust Optimization Considering the Uncertainty of Sources and Loads in Virtual Power Plants","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4412567147","doi":"https://doi.org/10.1109/access.2025.3591459"},"language":"en","primary_location":{"id":"doi:10.1109/access.2025.3591459","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3591459","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2025.3591459","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108849110","display_name":"Shixun Qi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210088511","display_name":"Inner Mongolia Electric Power (China)","ror":"https://ror.org/0041szh84","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210088511"]},{"id":"https://openalex.org/I4210102494","display_name":"Inner Mongolia Electric Power Survey & Design Institute (China)","ror":"https://ror.org/01cg3n190","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210102494"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shixun Qi","raw_affiliation_strings":["Inner Mongolia Power Trading Center Company Ltd., Hohhot, China","Inner Mongolia Electricity Trading Center Co., Ltd, Hohhot, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inner Mongolia Power Trading Center Company Ltd., Hohhot, China","institution_ids":["https://openalex.org/I4210088511","https://openalex.org/I4210102494"]},{"raw_affiliation_string":"Inner Mongolia Electricity Trading Center Co., Ltd, Hohhot, China","institution_ids":["https://openalex.org/I4210102494","https://openalex.org/I4210088511"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100348822","display_name":"Duo Li","orcid":"https://orcid.org/0000-0002-9401-9188"},"institutions":[{"id":"https://openalex.org/I4210088511","display_name":"Inner Mongolia Electric Power (China)","ror":"https://ror.org/0041szh84","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210088511"]},{"id":"https://openalex.org/I4210102494","display_name":"Inner Mongolia Electric Power Survey & Design Institute (China)","ror":"https://ror.org/01cg3n190","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210102494"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Duo Li","raw_affiliation_strings":["Inner Mongolia Power Trading Center Company Ltd., Hohhot, China","Inner Mongolia Electricity Trading Center Co., Ltd, Hohhot, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inner Mongolia Power Trading Center Company Ltd., Hohhot, China","institution_ids":["https://openalex.org/I4210088511","https://openalex.org/I4210102494"]},{"raw_affiliation_string":"Inner Mongolia Electricity Trading Center Co., Ltd, Hohhot, China","institution_ids":["https://openalex.org/I4210102494","https://openalex.org/I4210088511"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072099064","display_name":"Liyong Hou","orcid":"https://orcid.org/0009-0008-3226-914X"},"institutions":[{"id":"https://openalex.org/I4210088511","display_name":"Inner Mongolia Electric Power (China)","ror":"https://ror.org/0041szh84","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210088511"]},{"id":"https://openalex.org/I4210102494","display_name":"Inner Mongolia Electric Power Survey & Design Institute (China)","ror":"https://ror.org/01cg3n190","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210102494"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liyong Hou","raw_affiliation_strings":["Inner Mongolia Power Trading Center Company Ltd., Hohhot, China","Inner Mongolia Electricity Trading Center Co., Ltd, Hohhot, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inner Mongolia Power Trading Center Company Ltd., Hohhot, China","institution_ids":["https://openalex.org/I4210088511","https://openalex.org/I4210102494"]},{"raw_affiliation_string":"Inner Mongolia Electricity Trading Center Co., Ltd, Hohhot, China","institution_ids":["https://openalex.org/I4210102494","https://openalex.org/I4210088511"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100701007","display_name":"Haili Wang","orcid":"https://orcid.org/0000-0001-5072-2261"},"institutions":[{"id":"https://openalex.org/I4210088511","display_name":"Inner Mongolia Electric Power (China)","ror":"https://ror.org/0041szh84","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210088511"]},{"id":"https://openalex.org/I4210102494","display_name":"Inner Mongolia Electric Power Survey & Design Institute (China)","ror":"https://ror.org/01cg3n190","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210102494"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haili Wang","raw_affiliation_strings":["Inner Mongolia Power Trading Center Company Ltd., Hohhot, China","Inner Mongolia Electricity Trading Center Co., Ltd, Hohhot, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inner Mongolia Power Trading Center Company Ltd., Hohhot, China","institution_ids":["https://openalex.org/I4210088511","https://openalex.org/I4210102494"]},{"raw_affiliation_string":"Inner Mongolia Electricity Trading Center Co., Ltd, Hohhot, China","institution_ids":["https://openalex.org/I4210102494","https://openalex.org/I4210088511"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100322561","display_name":"Xin Li","orcid":"https://orcid.org/0000-0001-9542-6335"},"institutions":[{"id":"https://openalex.org/I4210088511","display_name":"Inner Mongolia Electric Power (China)","ror":"https://ror.org/0041szh84","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210088511"]},{"id":"https://openalex.org/I4210102494","display_name":"Inner Mongolia Electric Power Survey & Design Institute (China)","ror":"https://ror.org/01cg3n190","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210102494"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Xin","raw_affiliation_strings":["Inner Mongolia Power Trading Center Company Ltd., Hohhot, China","Inner Mongolia Electricity Trading Center Co., Ltd, Hohhot, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inner Mongolia Power Trading Center Company Ltd., Hohhot, China","institution_ids":["https://openalex.org/I4210088511","https://openalex.org/I4210102494"]},{"raw_affiliation_string":"Inner Mongolia Electricity Trading Center Co., Ltd, Hohhot, China","institution_ids":["https://openalex.org/I4210102494","https://openalex.org/I4210088511"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016140533","display_name":"Yaojie Jin","orcid":null},"institutions":[{"id":"https://openalex.org/I4210088511","display_name":"Inner Mongolia Electric Power (China)","ror":"https://ror.org/0041szh84","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210088511"]},{"id":"https://openalex.org/I4210102494","display_name":"Inner Mongolia Electric Power Survey & Design Institute (China)","ror":"https://ror.org/01cg3n190","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210102494"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaojie Jin","raw_affiliation_strings":["Inner Mongolia Power Trading Center Company Ltd., Hohhot, China","Inner Mongolia Electricity Trading Center Co., Ltd, Hohhot, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inner Mongolia Power Trading Center Company Ltd., Hohhot, China","institution_ids":["https://openalex.org/I4210088511","https://openalex.org/I4210102494"]},{"raw_affiliation_string":"Inner Mongolia Electricity Trading Center Co., Ltd, Hohhot, China","institution_ids":["https://openalex.org/I4210102494","https://openalex.org/I4210088511"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001693753","display_name":"Yuanji Cai","orcid":"https://orcid.org/0000-0002-3889-7066"},"institutions":[{"id":"https://openalex.org/I4210095546","display_name":"Tsinghua Sichuan Energy Internet Research Institute","ror":"https://ror.org/00pkx4k51","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210095546"]},{"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":"Yuanji Cai","raw_affiliation_strings":["Sichuan Energy Internet Research Institute, Tsinghua University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sichuan Energy Internet Research Institute, Tsinghua University, Chengdu, China","institution_ids":["https://openalex.org/I4210095546","https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008763316","display_name":"Mingfei Ban","orcid":"https://orcid.org/0000-0003-0702-8295"},"institutions":[{"id":"https://openalex.org/I47689461","display_name":"Northeast Forestry University","ror":"https://ror.org/02yxnh564","country_code":"CN","type":"education","lineage":["https://openalex.org/I47689461"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingfei Ban","raw_affiliation_strings":["School of Computer and Control Engineering, Northeast Forestry University, Harbin, China"],"raw_orcid":"https://orcid.org/0000-0003-0702-8295","affiliations":[{"raw_affiliation_string":"School of Computer and Control Engineering, Northeast Forestry University, Harbin, China","institution_ids":["https://openalex.org/I47689461"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":5.0982,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.95638386,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"13","issue":null,"first_page":"132155","last_page":"132169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9639000296592712,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9639000296592712,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9050999879837036,"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/stage","display_name":"Stage (stratigraphy)","score":0.7037733793258667},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5754461288452148},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.45672541856765747},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4270560145378113},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.4268966317176819},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19578906893730164},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.09716677665710449}],"concepts":[{"id":"https://openalex.org/C146357865","wikidata":"https://www.wikidata.org/wiki/Q1123245","display_name":"Stage (stratigraphy)","level":2,"score":0.7037733793258667},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5754461288452148},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.45672541856765747},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4270560145378113},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.4268966317176819},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19578906893730164},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.09716677665710449},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2025.3591459","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3591459","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b41f2e5f94544f42be0c9a42880a6cff","is_oa":true,"landing_page_url":"https://doaj.org/article/b41f2e5f94544f42be0c9a42880a6cff","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 13, Pp 132155-132169 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2025.3591459","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3591459","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.7900000214576721,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W2005921355","https://openalex.org/W2522769817","https://openalex.org/W2801216117","https://openalex.org/W2888514579","https://openalex.org/W2911667489","https://openalex.org/W2989606762","https://openalex.org/W3000182642","https://openalex.org/W3012390780","https://openalex.org/W3015322982","https://openalex.org/W3087044390","https://openalex.org/W3154043991","https://openalex.org/W3170479104","https://openalex.org/W3190538400","https://openalex.org/W3204068569","https://openalex.org/W4200296800","https://openalex.org/W4206740298","https://openalex.org/W4213446856","https://openalex.org/W4220840576","https://openalex.org/W4226258754","https://openalex.org/W4281728790","https://openalex.org/W4283026012","https://openalex.org/W4285203271","https://openalex.org/W4293912500","https://openalex.org/W4297423469","https://openalex.org/W4320713032","https://openalex.org/W4367672353","https://openalex.org/W4379792611","https://openalex.org/W4385949022","https://openalex.org/W4386500769","https://openalex.org/W4396783974","https://openalex.org/W4396784062","https://openalex.org/W4398765284","https://openalex.org/W4400156704","https://openalex.org/W4402259386","https://openalex.org/W4402615554","https://openalex.org/W4407638303","https://openalex.org/W4408787505"],"related_works":["https://openalex.org/W3005017983","https://openalex.org/W2205708137","https://openalex.org/W3182145356","https://openalex.org/W3212504317","https://openalex.org/W1988872022","https://openalex.org/W3028487898","https://openalex.org/W2302257968","https://openalex.org/W4295680010","https://openalex.org/W3035069654","https://openalex.org/W2790022662"],"abstract_inverted_index":{"Virtual":[0],"power":[1,7,210,214],"plants":[2],"(VPPs)":[3],"aggregate":[4],"controllable":[5],"distributed":[6,9,13,105,177],"sources,":[8,12],"new":[10,25,39],"energy":[11,14,26,40,80,87,169],"storage":[15],"devices,":[16],"loads,":[17],"and":[18,42,48,67,91,94,118,130,136,159,170,212,220,254,263,288,306],"other":[19],"resources.":[20],"As":[21],"the":[22,32,35,49,61,72,82,86,92,98,112,116,119,123,144,151,165,184,191,200,221,240,248,258,264,267,286,291,297,304],"proportion":[23],"of":[24,34,37,63,74,78,85,114,125,147,155,167,224,290,300,309],"in":[27,172,229,303],"VPPs":[28,90,174,230,310],"continues":[29],"to":[30,142,189,246],"rise,":[31],"impacts":[33],"uncertainty":[36,228,236],"internal":[38],"output":[41,152,213],"load":[43,96,171,218],"have":[44],"become":[45,56],"increasingly":[46],"significant,":[47],"demand":[50,99,216],"for":[51,195],"flexible":[52,93],"resources":[53],"has":[54],"also":[55],"more":[57],"urgent.":[58],"To":[59],"address":[60],"challenges":[62],"system":[64,88,209],"operation":[65,308],"optimization":[66,107,180,271],"resource":[68],"allocation":[69],"caused":[70],"by":[71],"integration":[73],"a":[75,104,176,251,255,276],"large":[76],"amount":[77],"renewable":[79,168],"on":[81,97,183],"supply":[83],"side":[84],"into":[89,207,250,275],"changeable":[95],"side,":[100],"this":[101,162,301],"paper":[102],"proposes":[103],"robust":[106,179],"method":[108],"that":[109],"simultaneously":[110],"considers":[111],"uncertainties":[113,124,166],"both":[115],"source":[117],"load.":[120,160],"First,":[121],"regarding":[122],"wind":[126,156],"power,":[127,157],"photovoltaic":[128],"output,":[129],"load,":[131],"Monte":[132],"Carlo":[133],"scenario":[134,137],"sampling":[135],"reduction":[138],"methods":[139],"are":[140],"employed":[141],"depict":[143],"typical":[145],"scenarios":[146],"uncertainty,":[148],"thereby":[149],"determining":[150],"interval":[153],"ranges":[154],"photovoltaic,":[158],"On":[161],"basis,":[163],"considering":[164,312],"multiple":[173,225],"simultaneously,":[175],"two-stage":[178],"model":[181,205,249,302],"based":[182],"min-max-min":[185],"structure":[186],"is":[187,231,244,273],"established":[188],"obtain":[190],"optimal":[192],"dispatching":[193],"scheme":[194],"VPP":[196],"operating":[197],"costs":[198],"under":[199],"most":[201],"extreme":[202],"scenarios.":[203],"The":[204,227],"takes":[206],"account":[208],"balance":[211],"constraints,":[215,219],"response":[217],"interaction":[222],"constraints":[223],"VPPs.":[226],"handled":[232],"through":[233],"an":[234],"adjustable":[235],"control":[237],"factor.":[238],"Subsequently,":[239],"Benders":[241],"decomposition":[242],"algorithm":[243],"used":[245],"split":[247],"master":[252],"problem":[253,272],"subproblem.":[256],"Combining":[257],"duality":[259],"theory,":[260],"KKT":[261],"conditions,":[262],"Big-M":[265],"method,":[266],"inner":[268],"layer":[269],"max-min":[270],"transformed":[274],"mixed":[277],"integer":[278],"linear":[279],"programming":[280],"problem.":[281],"Finally,":[282],"numerical":[283],"simulations":[284],"verify":[285],"correctness":[287],"effectiveness":[289],"proposed":[292],"model,":[293],"as":[294,296],"well":[295],"positive":[298],"role":[299],"economic":[305],"low-cost":[307],"when":[311],"capacity":[313],"configuration.":[314]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
