{"id":"https://openalex.org/W2942297290","doi":"https://doi.org/10.1109/tr.2019.2893138","title":"Distributionally Robust Reliability Assessment for Transmission System Hardening Plan Under $N-k$ Security Criterion","display_name":"Distributionally Robust Reliability Assessment for Transmission System Hardening Plan Under $N-k$ Security Criterion","publication_year":2019,"publication_date":"2019-04-25","ids":{"openalex":"https://openalex.org/W2942297290","doi":"https://doi.org/10.1109/tr.2019.2893138","mag":"2942297290"},"language":"en","primary_location":{"id":"doi:10.1109/tr.2019.2893138","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2019.2893138","pdf_url":null,"source":{"id":"https://openalex.org/S87725633","display_name":"IEEE Transactions on Reliability","issn_l":"0018-9529","issn":["0018-9529","1558-1721"],"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 Reliability","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/A5053481032","display_name":"Ali Bagheri","orcid":"https://orcid.org/0000-0001-8132-0337"},"institutions":[{"id":"https://openalex.org/I115475287","display_name":"Oklahoma State University","ror":"https://ror.org/01g9vbr38","country_code":"US","type":"education","lineage":["https://openalex.org/I115475287"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ali Bagheri","raw_affiliation_strings":["Department of Management Science and Information Systems, Spears School of Business, Oklahoma State University, Stillwater, OK, USA"],"raw_orcid":"https://orcid.org/0000-0001-8132-0337","affiliations":[{"raw_affiliation_string":"Department of Management Science and Information Systems, Spears School of Business, Oklahoma State University, Stillwater, OK, USA","institution_ids":["https://openalex.org/I115475287"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023118241","display_name":"Chaoyue Zhao","orcid":"https://orcid.org/0000-0003-0442-2991"},"institutions":[{"id":"https://openalex.org/I115475287","display_name":"Oklahoma State University","ror":"https://ror.org/01g9vbr38","country_code":"US","type":"education","lineage":["https://openalex.org/I115475287"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chaoyue Zhao","raw_affiliation_strings":["School of Industrial Engineering and Management, Oklahoma State University, Stillwater, OK, USA"],"raw_orcid":"https://orcid.org/0000-0003-0442-2991","affiliations":[{"raw_affiliation_string":"School of Industrial Engineering and Management, Oklahoma State University, Stillwater, OK, USA","institution_ids":["https://openalex.org/I115475287"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I115475287"],"apc_list":null,"apc_paid":null,"fwci":4.1819,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.93744818,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"68","issue":"2","first_page":"653","last_page":"662"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11941","display_name":"Power System Reliability and Maintenance","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T11941","display_name":"Power System Reliability and Maintenance","score":0.9993000030517578,"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/T11807","display_name":"Infrastructure Resilience and Vulnerability Analysis","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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":0.993399977684021,"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/reliability-engineering","display_name":"Reliability engineering","score":0.7362774610519409},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.6052570939064026},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5801908373832703},{"id":"https://openalex.org/keywords/ambiguity","display_name":"Ambiguity","score":0.5793911218643188},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.5740837454795837},{"id":"https://openalex.org/keywords/cascading-failure","display_name":"Cascading failure","score":0.4784424602985382},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.44176214933395386},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4185490608215332},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.2355588674545288},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.19964486360549927},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1650770902633667},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13638368248939514}],"concepts":[{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.7362774610519409},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.6052570939064026},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5801908373832703},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.5793911218643188},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.5740837454795837},{"id":"https://openalex.org/C119323957","wikidata":"https://www.wikidata.org/wiki/Q5048226","display_name":"Cascading failure","level":4,"score":0.4784424602985382},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.44176214933395386},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4185490608215332},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2355588674545288},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.19964486360549927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1650770902633667},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13638368248939514},{"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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tr.2019.2893138","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2019.2893138","pdf_url":null,"source":{"id":"https://openalex.org/S87725633","display_name":"IEEE Transactions on Reliability","issn_l":"0018-9529","issn":["0018-9529","1558-1721"],"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 Reliability","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7742417644","display_name":null,"funder_award_id":"NSF-1662589","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8559112503","display_name":null,"funder_award_id":"NSF-1610935","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W567546891","https://openalex.org/W760153864","https://openalex.org/W1502876580","https://openalex.org/W1571403844","https://openalex.org/W1578978182","https://openalex.org/W1647779468","https://openalex.org/W1810122495","https://openalex.org/W1968355947","https://openalex.org/W1996774007","https://openalex.org/W2000143048","https://openalex.org/W2005246195","https://openalex.org/W2008002305","https://openalex.org/W2009511185","https://openalex.org/W2030743740","https://openalex.org/W2036624125","https://openalex.org/W2045950406","https://openalex.org/W2088542428","https://openalex.org/W2090422417","https://openalex.org/W2097771670","https://openalex.org/W2098716819","https://openalex.org/W2100935434","https://openalex.org/W2107622862","https://openalex.org/W2112949599","https://openalex.org/W2118097396","https://openalex.org/W2119303899","https://openalex.org/W2125755323","https://openalex.org/W2134632549","https://openalex.org/W2137999695","https://openalex.org/W2138615297","https://openalex.org/W2139478864","https://openalex.org/W2140193829","https://openalex.org/W2142052648","https://openalex.org/W2146016251","https://openalex.org/W2148112915","https://openalex.org/W2153561032","https://openalex.org/W2162368241","https://openalex.org/W2175357651","https://openalex.org/W2205708137","https://openalex.org/W2310130856","https://openalex.org/W2332401959","https://openalex.org/W2342709508","https://openalex.org/W2374131623","https://openalex.org/W2519739684","https://openalex.org/W2560214921","https://openalex.org/W2608031041","https://openalex.org/W2917783100","https://openalex.org/W3023554475","https://openalex.org/W3147033875"],"related_works":["https://openalex.org/W2353179089","https://openalex.org/W2355051428","https://openalex.org/W2373141077","https://openalex.org/W3159334627","https://openalex.org/W2168347047","https://openalex.org/W2038278056","https://openalex.org/W2378097750","https://openalex.org/W2532099551","https://openalex.org/W2155742919","https://openalex.org/W1914681266"],"abstract_inverted_index":{"Increasing":[0],"the":[1,33,44,47,66,69,80,85,91,95,107,112,117,126,129,135,160,175,188,191,197,201,215,233,236],"complexity":[2],"of":[3,23,46,68,87,97,106,109,128,137,162,179,190,235],"power":[4,9,70],"transmission":[5,71,192],"networks":[6,26],"has":[7],"led":[8],"systems":[10,230],"to":[11,15,64,93,101,124,196,231],"be":[12,151],"more":[13],"vulnerable":[14],"cascading":[16,51],"failures.":[17,52],"Thus,":[18],"hardening":[19,58],"and":[20,149,166,211,226],"reliability":[21,45,67,127,133,189],"assessment":[22],"such":[24,143],"complex":[25],"have":[27,102],"become":[28],"a":[29,57,103,121],"must.":[30],"In":[31,53,79],"addition,":[32],"commonly":[34],"used":[35],"N":[36,74],"-":[37,75],"1":[38],"security":[39,77],"criterion":[40],"does":[41],"not":[42],"guarantee":[43],"system":[48,72,92,193],"against":[49],"possible":[50],"this":[54,156],"paper,":[55,157],"given":[56],"plan,":[59],"we":[60,83,115,158,169,220],"develop":[61],"two":[62],"models":[63,207],"evaluate":[65,125],"under":[73],"k":[76],"criterion.":[78],"first":[81],"model,":[82,114],"quantify":[84],"probability":[86,144,161,177],"no":[88],"load-shedding":[89],"in":[90,111,155,200],"assess":[94],"possibility":[96],"load":[98],"curtailment.":[99],"Then,":[100,168],"better":[104],"insight":[105],"amount":[108],"load-shed":[110],"second":[113],"use":[116],"conditional":[118],"value-at-risk":[119],"as":[120,164,208],"risk":[122],"measure":[123],"system.":[130],"To":[131],"perform":[132],"assessment,":[134],"information":[136,145],"contingency":[138],"probabilities":[139],"is":[140,146],"required.":[141],"However,":[142],"usually":[147],"unknown":[148,165,176],"cannot":[150],"estimated":[152],"precisely.":[153],"Therefore,":[154],"assume":[159],"contingencies":[163],"ambiguous.":[167],"construct":[170],"an":[171],"ambiguity":[172,202],"set":[173],"for":[174],"distribution":[178,199],"contingencies.":[180],"Our":[181],"approaches":[182],"are":[183],"robust":[184],"because":[185],"they":[186],"analyze":[187],"with":[194],"respect":[195],"worst-case":[198],"set.":[203],"We":[204],"formulate":[205],"both":[206],"bilevel":[209],"programs":[210],"solve":[212],"them":[213],"using":[214],"Bender's":[216],"decomposition":[217],"technique.":[218],"Finally,":[219],"conduct":[221],"numerical":[222],"experiments":[223],"on":[224],"6-bus":[225],"IEEE":[227],"118-bus":[228],"test":[229],"show":[232],"effectiveness":[234],"proposed":[237],"approaches.":[238]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}