{"id":"https://openalex.org/W4407327782","doi":"https://doi.org/10.1007/s44196-025-00745-3","title":"Optimal AC Power Flow with Energy Storage and Renewable Energy: An Efficient RL Algorithm Capable of Handling Equality Constraints","display_name":"Optimal AC Power Flow with Energy Storage and Renewable Energy: An Efficient RL Algorithm Capable of Handling Equality Constraints","publication_year":2025,"publication_date":"2025-02-10","ids":{"openalex":"https://openalex.org/W4407327782","doi":"https://doi.org/10.1007/s44196-025-00745-3"},"language":"en","primary_location":{"id":"doi:10.1007/s44196-025-00745-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-025-00745-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-025-00745-3.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/s44196-025-00745-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074824754","display_name":"Mingde Liu","orcid":"https://orcid.org/0009-0006-1154-4400"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Mingde Liu","raw_affiliation_strings":["School of Electric Power Engineering, South China University of Technology, Guangzhou, 510640, China"],"affiliations":[{"raw_affiliation_string":"School of Electric Power Engineering, South China University of Technology, Guangzhou, 510640, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068873092","display_name":"Jianquan Zhu","orcid":"https://orcid.org/0000-0001-6701-4018"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianquan Zhu","raw_affiliation_strings":["School of Electric Power Engineering, South China University of Technology, Guangzhou, 510640, China"],"affiliations":[{"raw_affiliation_string":"School of Electric Power Engineering, South China University of Technology, Guangzhou, 510640, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018898756","display_name":"Mingbo Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingbo Liu","raw_affiliation_strings":["School of Electric Power Engineering, South China University of Technology, Guangzhou, 510640, China"],"affiliations":[{"raw_affiliation_string":"School of Electric Power Engineering, South China University of Technology, Guangzhou, 510640, China","institution_ids":["https://openalex.org/I90610280"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074824754"],"corresponding_institution_ids":["https://openalex.org/I90610280"],"apc_list":{"value":1390,"currency":"GBP","value_usd":1704},"apc_paid":{"value":1390,"currency":"GBP","value_usd":1704},"fwci":0.7576,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.69148535,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"18","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","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/T10454","display_name":"Optimal Power Flow Distribution","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/T10223","display_name":"Microgrid Control and Optimization","score":0.9993000030517578,"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/T10305","display_name":"Power System Optimization and Stability","score":0.9991000294685364,"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/power-flow","display_name":"Power flow","score":0.7625675797462463},{"id":"https://openalex.org/keywords/renewable-energy","display_name":"Renewable energy","score":0.6711576581001282},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6078577637672424},{"id":"https://openalex.org/keywords/energy-storage","display_name":"Energy storage","score":0.6078052520751953},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5228310227394104},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5069615840911865},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4886389374732971},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4627551734447479},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.42411452531814575},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26353830099105835},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.22440698742866516},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.1714181900024414},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09656327962875366},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0772733986377716}],"concepts":[{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.7625675797462463},{"id":"https://openalex.org/C188573790","wikidata":"https://www.wikidata.org/wiki/Q12705","display_name":"Renewable energy","level":2,"score":0.6711576581001282},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6078577637672424},{"id":"https://openalex.org/C73916439","wikidata":"https://www.wikidata.org/wiki/Q837718","display_name":"Energy storage","level":3,"score":0.6078052520751953},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5228310227394104},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5069615840911865},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4886389374732971},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4627551734447479},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.42411452531814575},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26353830099105835},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.22440698742866516},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.1714181900024414},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09656327962875366},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0772733986377716},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s44196-025-00745-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-025-00745-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-025-00745-3.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d6ec54e9b20a46b386d45215223c6e47","is_oa":true,"landing_page_url":"https://doaj.org/article/d6ec54e9b20a46b386d45215223c6e47","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Computational Intelligence Systems, Vol 18, Iss 1, Pp 1-38 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s44196-025-00745-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-025-00745-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-025-00745-3.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8600000143051147,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1477544716","display_name":null,"funder_award_id":"Guangdong","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1709975844","display_name":null,"funder_award_id":"2022A1515011","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2196125980","display_name":null,"funder_award_id":"2022A151501119","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G2259640258","display_name":null,"funder_award_id":"No.51977081","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2938777395","display_name":null,"funder_award_id":"51501119","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4488680036","display_name":null,"funder_award_id":"2022A15","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4713160512","display_name":null,"funder_award_id":"51977081","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5171723308","display_name":null,"funder_award_id":"011193","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7133641121","display_name":null,"funder_award_id":"2022A1515011193","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G7726157001","display_name":null,"funder_award_id":"Grant No.","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"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407327782.pdf","grobid_xml":"https://content.openalex.org/works/W4407327782.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W1569990960","https://openalex.org/W2004117002","https://openalex.org/W2115097216","https://openalex.org/W2158955690","https://openalex.org/W2164063344","https://openalex.org/W2314914111","https://openalex.org/W2344216936","https://openalex.org/W2781726626","https://openalex.org/W2885669798","https://openalex.org/W2898892341","https://openalex.org/W2911464544","https://openalex.org/W2926550755","https://openalex.org/W2952242647","https://openalex.org/W2963569896","https://openalex.org/W2971091630","https://openalex.org/W2998540693","https://openalex.org/W3006765757","https://openalex.org/W3015689570","https://openalex.org/W3031194307","https://openalex.org/W3047073136","https://openalex.org/W3088315405","https://openalex.org/W3092305369","https://openalex.org/W3097422301","https://openalex.org/W3108892825","https://openalex.org/W3156919398","https://openalex.org/W3163732867","https://openalex.org/W3185972474","https://openalex.org/W3203701738","https://openalex.org/W3208346261","https://openalex.org/W3212493140","https://openalex.org/W3217441506","https://openalex.org/W4206269615","https://openalex.org/W4211186495","https://openalex.org/W4223531947","https://openalex.org/W4236654622","https://openalex.org/W4310626627","https://openalex.org/W4312550982","https://openalex.org/W4320340663","https://openalex.org/W4379276060","https://openalex.org/W4382317755","https://openalex.org/W4387723775","https://openalex.org/W4387993618","https://openalex.org/W4388142546","https://openalex.org/W4390571829","https://openalex.org/W4392114294","https://openalex.org/W4402039968","https://openalex.org/W6600553734"],"related_works":["https://openalex.org/W3017124762","https://openalex.org/W3097919110","https://openalex.org/W2710710002","https://openalex.org/W2021194995","https://openalex.org/W4221107878","https://openalex.org/W4220683285","https://openalex.org/W4212924852","https://openalex.org/W3126713256","https://openalex.org/W3157762916","https://openalex.org/W3134438818"],"abstract_inverted_index":{"Using":[0],"energy":[1,11],"storage":[2],"to":[3,17,131,157],"solve":[4],"the":[5,23,47,86,93,96,103,121,128,133,139,146,154,159,164,168,199,212],"multiperiod":[6],"OPF":[7,32],"problem":[8],"for":[9],"renewable":[10],"fluctuation":[12],"is":[13,82,124,151],"an":[14,58,117],"effective":[15],"way":[16],"increase":[18,132],"operation":[19],"safety":[20],"and":[21,50,68,111,170,210],"reduce":[22,158],"cost":[24],"of":[25,73,88,95,105,142,161,163,180,201,216],"power":[26],"systems.":[27],"However,":[28],"in":[29,116,153,167,206],"solving":[30],"this":[31,106],"problem,":[33],"model-based":[34],"methods":[35,44,52,205,218],"cannot":[36,45],"accurately":[37],"model":[38],"uncertain":[39],"scenarios,":[40],"while":[41],"traditional":[42],"RL":[43,59,196,204,217],"satisfy":[46,108],"constraints":[48],"well,":[49],"both":[51],"have":[53],"limitations.":[54],"Therefore,":[55],"we":[56],"propose":[57],"method,":[60],"ERL-HC,":[61],"that":[62,84,186,219],"does":[63],"not":[64],"require":[65],"scene":[66],"modelling":[67],"can":[69,113,220],"handle":[70,221],"general":[71,194],"forms":[72],"physical":[74],"constraints.":[75,223],"First,":[76],"a":[77,89,189],"constraint":[78],"policy":[79],"network":[80,91,107,123],"(CPN)":[81],"proposed":[83],"corrects":[85],"output":[87],"neural":[90],"on":[92,127,177],"basis":[94],"inequality":[97,165],"generalized":[98],"reduced":[99],"gradient":[100],"(GRG)":[101],"method;":[102],"outputs":[104],"all":[109],"constraints,":[110,209],"it":[112],"be":[114],"trained":[115],"end-to-end":[118],"manner.":[119],"Second,":[120],"critic":[122],"improved":[125],"based":[126],"IM":[129],"method":[130,150],"sample":[134],"learning":[135,191],"efficiency":[136],"by":[137],"improving":[138],"agent's":[140],"understanding":[141],"state":[143],"interdependencies.":[144],"Finally,":[145],"adaptive-tuning":[147],"Lagrange":[148],"multiplier":[149],"applied":[152],"AC":[155],"framework":[156],"number":[160],"iterations":[162],"GRG":[166],"CPN":[169],"efficiently":[171],"train":[172],"ERL-HC.":[173],"ERL-HC":[174,187],"was":[175],"tested":[176],"two":[178],"systems":[179],"different":[181],"sizes.":[182],"The":[183],"results":[184],"show":[185],"has":[188],"better":[190],"ability":[192],"than":[193],"safe":[195,203],"algorithms,":[197],"overcomes":[198],"limitations":[200],"mainstream":[202],"handling":[207],"equality":[208,222],"addresses":[211],"poor":[213],"generalization":[214],"issues":[215]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-22T08:09:32.410652","created_date":"2025-10-10T00:00:00"}