{"id":"https://openalex.org/W3097500757","doi":"https://doi.org/10.1109/tsg.2022.3154151","title":"Chance-Constrained OPF in Droop-Controlled Microgrids With Power Flow Routers","display_name":"Chance-Constrained OPF in Droop-Controlled Microgrids With Power Flow Routers","publication_year":2022,"publication_date":"2022-02-25","ids":{"openalex":"https://openalex.org/W3097500757","doi":"https://doi.org/10.1109/tsg.2022.3154151","mag":"3097500757"},"language":"en","primary_location":{"id":"doi:10.1109/tsg.2022.3154151","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2022.3154151","pdf_url":null,"source":{"id":"https://openalex.org/S59604973","display_name":"IEEE Transactions on Smart Grid","issn_l":"1949-3053","issn":["1949-3053","1949-3061"],"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 Smart Grid","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/A5054835816","display_name":"Chen Tian-Lun","orcid":"https://orcid.org/0000-0002-6407-9462"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Tianlun Chen","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015605407","display_name":"Yue Song","orcid":"https://orcid.org/0000-0002-4757-6862"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Yue Song","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062944003","display_name":"David J. Hill","orcid":"https://orcid.org/0000-0003-4036-0839"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["AU","HK"],"is_corresponding":false,"raw_author_name":"David J. Hill","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong","School of Electrical Engineering and Telecommunications, The University of New South Wales, Kensington, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I889458895"]},{"raw_affiliation_string":"School of Electrical Engineering and Telecommunications, The University of New South Wales, Kensington, NSW, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050605025","display_name":"Albert Y. S. Lam","orcid":"https://orcid.org/0000-0002-6887-9301"},"institutions":[{"id":"https://openalex.org/I4210090344","display_name":"Fano Labs (China)","ror":"https://ror.org/008jsgk36","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210090344"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Albert Y. S. Lam","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong","Fano Labs, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I889458895"]},{"raw_affiliation_string":"Fano Labs, Hong Kong","institution_ids":["https://openalex.org/I4210090344"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5054835816"],"corresponding_institution_ids":["https://openalex.org/I889458895"],"apc_list":null,"apc_paid":null,"fwci":1.9211,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.85335034,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"13","issue":"4","first_page":"2601","last_page":"2613"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","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/T10454","display_name":"Optimal Power Flow Distribution","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/T10223","display_name":"Microgrid Control and Optimization","score":0.9997000098228455,"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":0.9997000098228455,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/voltage-droop","display_name":"Voltage droop","score":0.7997888922691345},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6766290664672852},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.5293940901756287},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.501800537109375},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4834464490413666},{"id":"https://openalex.org/keywords/economic-dispatch","display_name":"Economic dispatch","score":0.4739145040512085},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.4693976938724518},{"id":"https://openalex.org/keywords/ac-power","display_name":"AC power","score":0.4439558982849121},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.38607582449913025},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.2909637689590454},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.24762746691703796},{"id":"https://openalex.org/keywords/voltage-source","display_name":"Voltage source","score":0.2108740508556366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.17554885149002075},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11877602338790894},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09554672241210938},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.08895924687385559}],"concepts":[{"id":"https://openalex.org/C40760162","wikidata":"https://www.wikidata.org/wiki/Q10920295","display_name":"Voltage droop","level":4,"score":0.7997888922691345},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6766290664672852},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.5293940901756287},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.501800537109375},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4834464490413666},{"id":"https://openalex.org/C187633118","wikidata":"https://www.wikidata.org/wiki/Q1317949","display_name":"Economic dispatch","level":4,"score":0.4739145040512085},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.4693976938724518},{"id":"https://openalex.org/C108755667","wikidata":"https://www.wikidata.org/wiki/Q1930258","display_name":"AC power","level":3,"score":0.4439558982849121},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.38607582449913025},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2909637689590454},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.24762746691703796},{"id":"https://openalex.org/C144655898","wikidata":"https://www.wikidata.org/wiki/Q1161128","display_name":"Voltage source","level":3,"score":0.2108740508556366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.17554885149002075},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11877602338790894},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09554672241210938},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.08895924687385559},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsg.2022.3154151","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2022.3154151","pdf_url":null,"source":{"id":"https://openalex.org/S59604973","display_name":"IEEE Transactions on Smart Grid","issn_l":"1949-3053","issn":["1949-3053","1949-3061"],"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 Smart Grid","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8399999737739563}],"awards":[{"id":"https://openalex.org/G1196506358","display_name":null,"funder_award_id":"17209219","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G6238690155","display_name":null,"funder_award_id":"17207918","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"}],"funders":[{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W1502540576","https://openalex.org/W1504052325","https://openalex.org/W1571403844","https://openalex.org/W1858422019","https://openalex.org/W1965408066","https://openalex.org/W1966751624","https://openalex.org/W2000587848","https://openalex.org/W2009704558","https://openalex.org/W2053072417","https://openalex.org/W2074663062","https://openalex.org/W2086691266","https://openalex.org/W2093909370","https://openalex.org/W2103565957","https://openalex.org/W2106424475","https://openalex.org/W2111919291","https://openalex.org/W2118550318","https://openalex.org/W2132833284","https://openalex.org/W2170736358","https://openalex.org/W2178935672","https://openalex.org/W2213135968","https://openalex.org/W2286169807","https://openalex.org/W2312939748","https://openalex.org/W2327238720","https://openalex.org/W2340306861","https://openalex.org/W2397371338","https://openalex.org/W2555142941","https://openalex.org/W2572169820","https://openalex.org/W2590657229","https://openalex.org/W2593081246","https://openalex.org/W2596530326","https://openalex.org/W2625248137","https://openalex.org/W2760578628","https://openalex.org/W2768852899","https://openalex.org/W2795842538","https://openalex.org/W2801646001","https://openalex.org/W2883548103","https://openalex.org/W2900130645","https://openalex.org/W2954646619","https://openalex.org/W2962752356","https://openalex.org/W2962850894","https://openalex.org/W2963669827","https://openalex.org/W2964119122","https://openalex.org/W2964172516","https://openalex.org/W2964266044","https://openalex.org/W2964289666","https://openalex.org/W2974739011","https://openalex.org/W3031726291","https://openalex.org/W3032715021","https://openalex.org/W3097981256","https://openalex.org/W3133628981","https://openalex.org/W4256550092","https://openalex.org/W6695842710","https://openalex.org/W6778766488"],"related_works":["https://openalex.org/W2523432015","https://openalex.org/W2765340260","https://openalex.org/W2153130273","https://openalex.org/W3023710910","https://openalex.org/W2076823813","https://openalex.org/W3008686614","https://openalex.org/W2143080380","https://openalex.org/W1589163333","https://openalex.org/W2060924671","https://openalex.org/W3134658563"],"abstract_inverted_index":{"High":[0],"penetration":[1],"of":[2,62,92,128,177],"renewable":[3,24,102],"generation":[4],"poses":[5],"challenges":[6],"to":[7,12,48,58,69,97,115,147,182],"power":[8,39,44,71,82,95],"system":[9,99,165,190],"operation":[10],"due":[11],"its":[13],"uncertain":[14],"nature.":[15],"In":[16],"droop-controlled":[17],"microgrids,":[18],"the":[19,29,51,70,75,85,117,126,131,167,174,184,189],"voltage":[20,52,178,185],"volatility":[21],"induced":[22],"by":[23,28,120],"uncertainties":[25],"is":[26,145,158],"aggravated":[27],"high":[30],"droop":[31],"gains.":[32],"This":[33],"paper":[34],"proposes":[35],"a":[36,59,89,105,123,141,152,161,193],"chance-constrained":[37],"optimal":[38],"flow":[40,45],"(CC-OPF)":[41],"problem":[42,119],"with":[43,74],"routers":[46],"(PFRs)":[47],"better":[49],"regulate":[50],"profile":[53],"in":[54,192],"microgrids.":[55],"PFR":[56],"refers":[57],"general":[60],"type":[61],"network-side":[63],"controller":[64],"that":[65,78,170],"brings":[66],"more":[67,194],"flexibility":[68,83],"network.":[72],"Comparing":[73],"normal":[76],"CC-OPF":[77,118],"relies":[79],"on":[80,160],"node":[81],"only,":[84],"proposed":[86,156],"model":[87],"introduces":[88],"new":[90],"dimension":[91],"control":[93],"from":[94],"network":[96],"enhance":[98],"performance":[100],"under":[101],"uncertainties.":[103],"Adopting":[104],"partial":[106],"linearization":[107],"method":[108,157],"and":[109,133,166,180,196],"an":[110],"iterative":[111],"algorithm":[112],"allows":[113],"us":[114],"address":[116],"iteratively":[121],"solving":[122],"subproblem.":[124],"Since":[125],"inclusion":[127],"PFRs":[129,171],"complicates":[130],"subproblem":[132,150],"makes":[134,188],"common":[135],"solvers":[136],"no":[137],"longer":[138],"applicable":[139],"directly,":[140],"semidefinite":[142],"programming":[143],"relaxation":[144],"used":[146],"transform":[148],"each":[149],"into":[151],"convex":[153],"form.":[154],"The":[155],"verified":[159],"modified":[162],"IEEE":[163],"33-bus":[164],"results":[168],"show":[169],"significantly":[172],"reduce":[173],"standard":[175],"deviations":[176],"magnitudes":[179],"contribute":[181],"mitigating":[183],"volatility,":[186],"which":[187],"operate":[191],"economic":[195],"secure":[197],"way.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
