{"id":"https://openalex.org/W2897628126","doi":"https://doi.org/10.1007/s40565-018-0462-9","title":"Interval optimal power flow applied to distribution networks under uncertainty of loads and renewable resources","display_name":"Interval optimal power flow applied to distribution networks under uncertainty of loads and renewable resources","publication_year":2018,"publication_date":"2018-10-16","ids":{"openalex":"https://openalex.org/W2897628126","doi":"https://doi.org/10.1007/s40565-018-0462-9","mag":"2897628126"},"language":"en","primary_location":{"id":"doi:10.1007/s40565-018-0462-9","doi":"https://doi.org/10.1007/s40565-018-0462-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40565-018-0462-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40565-018-0462-9.pdf","source":{"id":"https://openalex.org/S4210194934","display_name":"Journal of Modern Power Systems and Clean Energy","issn_l":"2196-5420","issn":["2196-5420","2196-5625"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-100","russia-white-list-1"],"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Modern Power Systems and Clean Energy","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://link.springer.com/content/pdf/10.1007/s40565-018-0462-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103003628","display_name":"Pengwei Chen","orcid":"https://orcid.org/0000-0003-4461-6192","observed_orcids":["https://orcid.org/0000-0003-4461-6192"]},"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":true,"raw_author_name":"Pengwei CHEN","raw_affiliation_strings":["North China Electric Power University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-4461-6192","affiliations":[{"raw_affiliation_string":"North China Electric Power University, Beijing, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102102608","display_name":"Xiangning Xiao","orcid":null,"observed_orcids":[]},"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":"Xiangning XIAO","raw_affiliation_strings":["North China Electric Power University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"North China Electric Power University, Beijing, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100743065","display_name":"Xuhui Wang","orcid":"https://orcid.org/0000-0002-3937-0717","observed_orcids":["https://orcid.org/0000-0002-3937-0717"]},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuhui WANG","raw_affiliation_strings":["Hefei University of Technology, Hefei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hefei University of Technology, Hefei, China","institution_ids":["https://openalex.org/I16365422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103003628"],"corresponding_institution_ids":["https://openalex.org/I153473198"],"apc_list":null,"apc_paid":null,"fwci":0.7655,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.69992163,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"7","issue":"1","first_page":"139","last_page":"150"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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"}},{"id":"https://openalex.org/T10424","display_name":"Electric Power System Optimization","score":0.0027000000700354576,"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/T10305","display_name":"Power System Optimization and Stability","score":0.00039999998989515007,"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/distribution-networks","display_name":"distribution networks","score":0.9210000038146973},{"id":"https://openalex.org/keywords/load-uncertainty","display_name":"load uncertainty","score":0.7749999761581421},{"id":"https://openalex.org/keywords/renewable-energy-uncertainty","display_name":"renewable energy uncertainty","score":0.8989999890327454},{"id":"https://openalex.org/keywords/affine-arithmetic","display_name":"affine arithmetic","score":0.9760000109672546},{"id":"https://openalex.org/keywords/second-order-cone-programming","display_name":"second-order cone programming","score":0.9990000128746033},{"id":"https://openalex.org/keywords/active-distribution-networks","display_name":"active distribution networks","score":0.8379999995231628},{"id":"https://openalex.org/keywords/energy-dispatching","display_name":"energy dispatching","score":0.6850000023841858}],"concepts":[{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.7232943773269653},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6991075873374939},{"id":"https://openalex.org/C167315692","wikidata":"https://www.wikidata.org/wiki/Q3622729","display_name":"Affine arithmetic","level":3,"score":0.6788816452026367},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.6399261355400085},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5713032484054565},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.5520822405815125},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5323448777198792},{"id":"https://openalex.org/C188573790","wikidata":"https://www.wikidata.org/wiki/Q12705","display_name":"Renewable energy","level":2,"score":0.4943265914916992},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4856756925582886},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4563804268836975},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.4165477156639099},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34147292375564575},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.3392658233642578},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25710529088974},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.16160711646080017},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"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/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/s40565-018-0462-9","doi":"https://doi.org/10.1007/s40565-018-0462-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40565-018-0462-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40565-018-0462-9.pdf","source":{"id":"https://openalex.org/S4210194934","display_name":"Journal of Modern Power Systems and Clean Energy","issn_l":"2196-5420","issn":["2196-5420","2196-5625"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-100","russia-white-list-1"],"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Modern Power Systems and Clean Energy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:99c046a3cc80402388f708b0a2c7b721","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/99c046a3cc80402388f708b0a2c7b721","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,"listed_in":[],"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":"Journal of Modern Power Systems and Clean Energy, Vol 7, Iss 1, Pp 139-150 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s40565-018-0462-9","doi":"https://doi.org/10.1007/s40565-018-0462-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40565-018-0462-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40565-018-0462-9.pdf","source":{"id":"https://openalex.org/S4210194934","display_name":"Journal of Modern Power Systems and Clean Energy","issn_l":"2196-5420","issn":["2196-5420","2196-5625"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-100","russia-white-list-1"],"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Modern Power Systems and Clean Energy","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":1.0},{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.9090999960899353}],"study_designs":[],"awards":[{"id":"https://openalex.org/G1357094807","display_name":null,"funder_award_id":"61772167","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4148671902","display_name":null,"funder_award_id":"2016XS02","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2897628126.pdf","grobid_xml":"https://content.openalex.org/works/W2897628126.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W139049954","https://openalex.org/W1981882279","https://openalex.org/W1992644581","https://openalex.org/W1997067397","https://openalex.org/W2008297212","https://openalex.org/W2011226720","https://openalex.org/W2029436805","https://openalex.org/W2031742518","https://openalex.org/W2038214601","https://openalex.org/W2044632916","https://openalex.org/W2063559372","https://openalex.org/W2065846084","https://openalex.org/W2074628584","https://openalex.org/W2078329246","https://openalex.org/W2093909370","https://openalex.org/W2094855429","https://openalex.org/W2107846845","https://openalex.org/W2108142964","https://openalex.org/W2131798279","https://openalex.org/W2132833284","https://openalex.org/W2145761514","https://openalex.org/W2152556073","https://openalex.org/W2156324709","https://openalex.org/W2167067930","https://openalex.org/W2169884274","https://openalex.org/W2172200392","https://openalex.org/W2213622842","https://openalex.org/W2314462582","https://openalex.org/W2328368818","https://openalex.org/W2344216936","https://openalex.org/W2345054075","https://openalex.org/W2461951329","https://openalex.org/W2514218015","https://openalex.org/W2572169820","https://openalex.org/W2586661589","https://openalex.org/W2593081246","https://openalex.org/W3097981256","https://openalex.org/W3101868728","https://openalex.org/W4241079583"],"related_works":["https://openalex.org/W2794550251","https://openalex.org/W4386056891","https://openalex.org/W2520152490","https://openalex.org/W2595255641","https://openalex.org/W3093547543","https://openalex.org/W4409175031","https://openalex.org/W2790148886","https://openalex.org/W4324360602","https://openalex.org/W3153514892","https://openalex.org/W3110908232"],"abstract_inverted_index":{"Optimal":[0],"power":[1,36],"flow":[2,37],"(OPF)":[3],"has":[4],"been":[5],"used":[6],"for":[7],"energy":[8],"dispatching":[9],"in":[10],"active":[11],"distribution":[12,90],"networks.":[13],"To":[14],"satisfy":[15],"constraints":[16],"fully":[17],"and":[18,28,43,56,76,86,95],"achieve":[19],"strict":[20],"operational":[21],"bounds":[22],"under":[23],"the":[24,93,98],"uncertainties":[25],"from":[26],"loads":[27],"sources,":[29],"this":[30],"paper":[31],"derives":[32],"an":[33],"interval":[34,44],"optimal":[35],"(I-OPF)":[38],"method":[39,50],"employing":[40],"affine":[41],"arithmetic":[42],"Taylor":[45],"expansion.":[46],"An":[47],"enhanced":[48],"I-OPF":[49],"based":[51],"on":[52,80],"successive":[53],"linear":[54],"approximation":[55],"second-order":[57],"cone":[58],"programming":[59],"is":[60],"developed":[61],"to":[62],"improve":[63],"solution":[64],"accuracy.":[65],"The":[66],"proposed":[67,99],"methods":[68],"are":[69],"benchmarked":[70],"against":[71],"Monte":[72],"Carlo":[73],"simulation":[74],"(MCS)":[75],"stochastic":[77],"OPF.":[78],"Tests":[79],"a":[81,87],"modified":[82],"IEEE":[83],"33-bus":[84],"system":[85],"real":[88],"113-bus":[89],"network":[91],"validate":[92],"effectiveness":[94],"applicability":[96],"of":[97],"methods.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2018-10-26T00:00:00"}