{"id":"https://openalex.org/W2794376382","doi":"https://doi.org/10.1109/tsg.2018.2814584","title":"Mathematical Base and Deduction of Security Region for Distribution Systems With DER","display_name":"Mathematical Base and Deduction of Security Region for Distribution Systems With DER","publication_year":2018,"publication_date":"2018-03-12","ids":{"openalex":"https://openalex.org/W2794376382","doi":"https://doi.org/10.1109/tsg.2018.2814584","mag":"2794376382"},"language":"en","primary_location":{"id":"doi:10.1109/tsg.2018.2814584","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2018.2814584","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/A5015972267","display_name":"Guoqiang Zu","orcid":"https://orcid.org/0000-0003-4230-4419"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guoqiang Zu","raw_affiliation_strings":["Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101691155","display_name":"Jun Xiao","orcid":"https://orcid.org/0000-0002-1762-8203"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Xiao","raw_affiliation_strings":["Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066245188","display_name":"Kai Sun","orcid":"https://orcid.org/0000-0002-0305-2725"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kai Sun","raw_affiliation_strings":["Department of EECS, University of Tennessee, Knoxville, TN, USA"],"affiliations":[{"raw_affiliation_string":"Department of EECS, University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015972267"],"corresponding_institution_ids":["https://openalex.org/I162868743"],"apc_list":null,"apc_paid":null,"fwci":3.5515,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.93156198,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"10","issue":"3","first_page":"2892","last_page":"2903"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10917","display_name":"Smart Grid Security and Resilience","score":0.9983999729156494,"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/T10917","display_name":"Smart Grid Security and Resilience","score":0.9983999729156494,"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/T10454","display_name":"Optimal Power Flow Distribution","score":0.9969000220298767,"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":0.9954000115394592,"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/computer-science","display_name":"Computer science","score":0.5275464057922363},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.45776063203811646},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.449015349149704},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3352063298225403},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3247682750225067},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3081445097923279},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12785300612449646}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5275464057922363},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.45776063203811646},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.449015349149704},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3352063298225403},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3247682750225067},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3081445097923279},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12785300612449646},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsg.2018.2814584","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2018.2814584","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":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8600000143051147}],"awards":[{"id":"https://openalex.org/G3876566573","display_name":null,"funder_award_id":"2016YFB0900103","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G7725357788","display_name":null,"funder_award_id":"51477112","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/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1521605399","https://openalex.org/W1669532953","https://openalex.org/W1932011969","https://openalex.org/W1951422684","https://openalex.org/W1965247304","https://openalex.org/W1974921713","https://openalex.org/W2002506366","https://openalex.org/W2003622332","https://openalex.org/W2009625847","https://openalex.org/W2058893579","https://openalex.org/W2069817859","https://openalex.org/W2079414984","https://openalex.org/W2098132429","https://openalex.org/W2103768761","https://openalex.org/W2122249513","https://openalex.org/W2142238016","https://openalex.org/W2168343807","https://openalex.org/W2169714359","https://openalex.org/W2344311391","https://openalex.org/W2500727282","https://openalex.org/W2620007478","https://openalex.org/W3145585884","https://openalex.org/W4253303466"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"This":[0],"paper":[1,44],"presents":[2],"the":[3,19,25,29,35,46,70,91,100,108,111,113,120],"mathematical":[4,48,65,116],"definition":[5,49],"and":[6,82,115],"deduction":[7,117],"for":[8,18,125],"distribution":[9,40,94,127],"system":[10,95],"security":[11,72,123],"region":[12,124],"(DSSR),":[13],"which":[14,52,77],"lays":[15],"a":[16,39,55,60,87],"foundation":[17],"DSSR":[20,23,78],"theory.":[21],"The":[22],"is":[24,73,79,83,104],"set":[26,56],"of":[27,38,50,90,122],"all":[28],"N-1":[30,71],"secure":[31],"operating":[32],"points":[33],"in":[34,107],"state":[36],"space":[37],"system.":[41,128],"First,":[42],"this":[43],"proposes":[45],"strict":[47],"DSSR,":[51],"defines":[53],"that":[54],"can":[57],"be":[58],"called":[59],"\u201cregion\u201d":[61],"only":[62],"if":[63],"three":[64],"conditions":[66],"are":[67],"satisfied.":[68],"Then,":[69],"deducted,":[74],"based":[75],"on":[76],"proved":[80],"existing":[81],"mathematically":[84],"deducted.":[85],"As":[86],"basic":[88],"feature":[89],"future":[92],"smart":[93],"with":[96],"distributed":[97],"energy":[98],"resources,":[99],"bidirectional":[101],"power":[102],"flow":[103],"fully":[105],"considered":[106],"deduction.":[109],"In":[110],"conclusion,":[112],"observation":[114],"both":[118],"show":[119],"existence":[121],"any":[126]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":5}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}