{"id":"https://openalex.org/W4409706431","doi":"https://doi.org/10.3390/sym17050632","title":"Multi-Stage Stochastic Planning for Transmission Systems Considering Dynamic Frequency Stability","display_name":"Multi-Stage Stochastic Planning for Transmission Systems Considering Dynamic Frequency Stability","publication_year":2025,"publication_date":"2025-04-23","ids":{"openalex":"https://openalex.org/W4409706431","doi":"https://doi.org/10.3390/sym17050632"},"language":"en","primary_location":{"id":"doi:10.3390/sym17050632","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17050632","pdf_url":"https://www.mdpi.com/2073-8994/17/5/632/pdf?version=1745390311","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/5/632/pdf?version=1745390311","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000154817","display_name":"Xiaoming Luan","orcid":"https://orcid.org/0000-0002-9699-0322"},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]},{"id":"https://openalex.org/I4392738113","display_name":"China Electric Power Research Institute","ror":"https://ror.org/05ehpzy81","country_code":null,"type":"facility","lineage":["https://openalex.org/I17442442","https://openalex.org/I4392738113"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoming Luan","raw_affiliation_strings":["China Electric Power Research Institute, Beijing 100192, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China Electric Power Research Institute, Beijing 100192, China","institution_ids":["https://openalex.org/I153473198","https://openalex.org/I4392738113"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100959456","display_name":"Huadong Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]},{"id":"https://openalex.org/I4392738113","display_name":"China Electric Power Research Institute","ror":"https://ror.org/05ehpzy81","country_code":null,"type":"facility","lineage":["https://openalex.org/I17442442","https://openalex.org/I4392738113"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huadong Sun","raw_affiliation_strings":["China Electric Power Research Institute, Beijing 100192, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China Electric Power Research Institute, Beijing 100192, China","institution_ids":["https://openalex.org/I153473198","https://openalex.org/I4392738113"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085101386","display_name":"Guoliang Zhao","orcid":"https://orcid.org/0000-0002-0323-1299"},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]},{"id":"https://openalex.org/I4392738113","display_name":"China Electric Power Research Institute","ror":"https://ror.org/05ehpzy81","country_code":null,"type":"facility","lineage":["https://openalex.org/I17442442","https://openalex.org/I4392738113"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guoliang Zhao","raw_affiliation_strings":["China Electric Power Research Institute, Beijing 100192, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China Electric Power Research Institute, Beijing 100192, China","institution_ids":["https://openalex.org/I153473198","https://openalex.org/I4392738113"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100922737","display_name":"Guangyao Qiao","orcid":null},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]},{"id":"https://openalex.org/I4392738113","display_name":"China Electric Power Research Institute","ror":"https://ror.org/05ehpzy81","country_code":null,"type":"facility","lineage":["https://openalex.org/I17442442","https://openalex.org/I4392738113"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangyao Qiao","raw_affiliation_strings":["China Electric Power Research Institute, Beijing 100192, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China Electric Power Research Institute, Beijing 100192, China","institution_ids":["https://openalex.org/I153473198","https://openalex.org/I4392738113"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029726063","display_name":"Zhengang Lu","orcid":"https://orcid.org/0000-0001-6490-5819"},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]},{"id":"https://openalex.org/I4392738113","display_name":"China Electric Power Research Institute","ror":"https://ror.org/05ehpzy81","country_code":null,"type":"facility","lineage":["https://openalex.org/I17442442","https://openalex.org/I4392738113"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengang Lu","raw_affiliation_strings":["China Electric Power Research Institute, Beijing 100192, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China Electric Power Research Institute, Beijing 100192, China","institution_ids":["https://openalex.org/I153473198","https://openalex.org/I4392738113"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100570378","display_name":"Yunfei Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]},{"id":"https://openalex.org/I4392738113","display_name":"China Electric Power Research Institute","ror":"https://ror.org/05ehpzy81","country_code":null,"type":"facility","lineage":["https://openalex.org/I17442442","https://openalex.org/I4392738113"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunfei Xu","raw_affiliation_strings":["China Electric Power Research Institute, Beijing 100192, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China Electric Power Research Institute, Beijing 100192, China","institution_ids":["https://openalex.org/I153473198","https://openalex.org/I4392738113"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100770262","display_name":"Weiguo Li","orcid":"https://orcid.org/0009-0000-0509-6900"},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]},{"id":"https://openalex.org/I4392738113","display_name":"China Electric Power Research Institute","ror":"https://ror.org/05ehpzy81","country_code":null,"type":"facility","lineage":["https://openalex.org/I17442442","https://openalex.org/I4392738113"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weiguo Li","raw_affiliation_strings":["China Electric Power Research Institute, Beijing 100192, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China Electric Power Research Institute, Beijing 100192, China","institution_ids":["https://openalex.org/I153473198","https://openalex.org/I4392738113"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101922977","display_name":"Tao Zheng","orcid":"https://orcid.org/0000-0002-7706-7831"},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Zheng","raw_affiliation_strings":["School of Electrical and Electronic Engineering, North China Electric Power University, Beijing 102206, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, North China Electric Power University, Beijing 102206, China","institution_ids":["https://openalex.org/I153473198"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085101386"],"corresponding_institution_ids":["https://openalex.org/I153473198","https://openalex.org/I4392738113"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04897328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"5","first_page":"632","last_page":"632"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10424","display_name":"Electric Power System Optimization","score":0.9990000128746033,"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/T10424","display_name":"Electric Power System Optimization","score":0.9990000128746033,"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/T11941","display_name":"Power System Reliability and Maintenance","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"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/T10454","display_name":"Optimal Power Flow Distribution","score":0.9955999851226807,"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/stability","display_name":"Stability (learning theory)","score":0.59157395362854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5586689114570618},{"id":"https://openalex.org/keywords/stage","display_name":"Stage (stratigraphy)","score":0.5139622092247009},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4723086357116699},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.45420026779174805},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33558323979377747},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2573893964290619},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.18479537963867188},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.14139309525489807},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.11018788814544678},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08485999703407288}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.59157395362854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5586689114570618},{"id":"https://openalex.org/C146357865","wikidata":"https://www.wikidata.org/wiki/Q1123245","display_name":"Stage (stratigraphy)","level":2,"score":0.5139622092247009},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4723086357116699},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.45420026779174805},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33558323979377747},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2573893964290619},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.18479537963867188},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.14139309525489807},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.11018788814544678},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08485999703407288},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17050632","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17050632","pdf_url":"https://www.mdpi.com/2073-8994/17/5/632/pdf?version=1745390311","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17050632","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17050632","pdf_url":"https://www.mdpi.com/2073-8994/17/5/632/pdf?version=1745390311","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4939834413","display_name":null,"funder_award_id":"5100-202355385A-2-3-XG","funder_id":"https://openalex.org/F4320335967","funder_display_name":"Science and Technology Project of State Grid"}],"funders":[{"id":"https://openalex.org/F4320326707","display_name":"State Grid Corporation of China","ror":"https://ror.org/05twwhs70"},{"id":"https://openalex.org/F4320335967","display_name":"Science and Technology Project of State Grid","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409706431.pdf","grobid_xml":"https://content.openalex.org/works/W4409706431.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W2132025983","https://openalex.org/W2737440646","https://openalex.org/W2744197839","https://openalex.org/W2802839291","https://openalex.org/W2905843731","https://openalex.org/W2971032911","https://openalex.org/W2972172223","https://openalex.org/W2989350759","https://openalex.org/W3036452959","https://openalex.org/W3093503624","https://openalex.org/W3136600829","https://openalex.org/W3165237440","https://openalex.org/W3190690934","https://openalex.org/W3200543552","https://openalex.org/W3205563420","https://openalex.org/W4285216778","https://openalex.org/W4293145644","https://openalex.org/W4293202919","https://openalex.org/W4309102586","https://openalex.org/W4323338527","https://openalex.org/W4385627096","https://openalex.org/W4396214947","https://openalex.org/W4399057771"],"related_works":["https://openalex.org/W2329386257","https://openalex.org/W2503350049","https://openalex.org/W2397616145","https://openalex.org/W1982160337","https://openalex.org/W2397320258","https://openalex.org/W1971380437","https://openalex.org/W1983548084","https://openalex.org/W2141691317","https://openalex.org/W2110846987","https://openalex.org/W4324058133"],"abstract_inverted_index":{"The":[0],"increasing":[1],"penetration":[2],"of":[3,13,30,67,101,125,177],"renewable":[4],"generations":[5,34],"(RGs)":[6],"poses":[7],"significant":[8],"challenges":[9],"to":[10,105,108,143,159],"the":[11,28,64,84,92,113,121,145,148,161,166,175,178],"operation":[12],"transmission":[14,55],"power":[15,56],"systems,":[16],"especially":[17],"for":[18,54],"not":[19],"only":[20,96],"steady-stage":[21],"uncertainties":[22,66,103],"but":[23],"also":[24],"dynamic-state":[25],"stability.":[26,62],"Hence,":[27],"symmetry":[29],"RGs":[31,68],"and":[32,91,127],"synchronous":[33],"(SGs)":[35],"should":[36],"be":[37],"improved":[38],"by":[39,88,137,164],"a":[40,47,74,138,152],"proper":[41],"planning":[42,50,93,110,149],"strategy.":[43],"For":[44],"this":[45,82],"purpose,":[46],"multi-stage":[48,75],"stochastic":[49,76],"method":[51,77,142],"is":[52,86,157],"proposed":[53,179],"systems":[57],"(TPSs)":[58],"considering":[59,120],"dynamic":[60,114],"frequency":[61,115,122],"Specifically,":[63],"progressive":[65,153],"over":[69,186],"stages":[70],"are":[71,95,118,131,189],"addressed":[72],"with":[73,78,134,147],"nonanticipativity":[79,106],"constraints.":[80],"In":[81],"scheme,":[83],"uncertainty":[85],"represented":[87],"probability-weighted":[89],"scenarios,":[90],"decisions":[94],"dependent":[97],"on":[98],"current":[99],"realizations":[100],"RG":[102],"according":[104],"constraints":[107,117,130],"improve":[109,144],"efficiency.":[111],"Moreover,":[112],"stability":[116],"derived":[119],"regulation":[123],"strategy":[124],"RGs,":[126],"these":[128],"nonconvex":[129],"further":[132],"linearized":[133],"high":[135],"accuracy":[136],"maximal":[139],"affine":[140],"function-based":[141],"compatibility":[146],"model.":[150],"Subsequently,":[151],"hedging":[154],"algorithm":[155],"(PHA)":[156],"designed":[158],"reduce":[160],"computational":[162],"burden":[163],"decomposing":[165],"multi-scenario":[167],"high-dimensional":[168],"model":[169],"into":[170],"multiple":[171],"small-scale":[172],"models.":[173],"Finally,":[174],"effectiveness":[176],"method,":[180],"as":[181,183],"well":[182],"its":[184],"superiority":[185],"existing":[187],"approaches,":[188],"validated":[190],"through":[191],"numerical":[192],"experiments.":[193]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
