{"id":"https://openalex.org/W2769996359","doi":"https://doi.org/10.1109/tsg.2017.2773603","title":"Chance Constrained Reserve Scheduling Using Uncertain Controllable Loads Part II: Analytical Reformulation","display_name":"Chance Constrained Reserve Scheduling Using Uncertain Controllable Loads Part II: Analytical Reformulation","publication_year":2017,"publication_date":"2017-11-15","ids":{"openalex":"https://openalex.org/W2769996359","doi":"https://doi.org/10.1109/tsg.2017.2773603","mag":"2769996359"},"language":"en","primary_location":{"id":"doi:10.1109/tsg.2017.2773603","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2017.2773603","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/A5100387288","display_name":"Bowen Li","orcid":"https://orcid.org/0000-0002-7789-6226"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bowen Li","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056169398","display_name":"Maria Vrakopoulou","orcid":"https://orcid.org/0000-0003-2937-5714"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Maria Vrakopoulou","raw_affiliation_strings":["Automatic Control Laboratory, ETH Zurich, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Automatic Control Laboratory, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015257057","display_name":"Johanna L. Mathieu","orcid":"https://orcid.org/0000-0001-8834-5350"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Johanna L. Mathieu","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100387288"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":3.7877,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.93951456,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"10","issue":"2","first_page":"1618","last_page":"1625"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10424","display_name":"Electric Power System Optimization","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"}},"topics":[{"id":"https://openalex.org/T10424","display_name":"Electric Power System Optimization","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"}},{"id":"https://openalex.org/T11052","display_name":"Energy Load and Power Forecasting","score":0.9973000288009644,"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/T10454","display_name":"Optimal Power Flow Distribution","score":0.996999979019165,"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/mathematical-optimization","display_name":"Mathematical optimization","score":0.696163535118103},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.6234411001205444},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.5699917078018188},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.5637520551681519},{"id":"https://openalex.org/keywords/power-flow","display_name":"Power flow","score":0.5592383146286011},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.547726571559906},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5244545936584473},{"id":"https://openalex.org/keywords/power-system-simulation","display_name":"Power system simulation","score":0.4918980598449707},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.317582905292511},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21397215127944946}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.696163535118103},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.6234411001205444},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.5699917078018188},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.5637520551681519},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.5592383146286011},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.547726571559906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5244545936584473},{"id":"https://openalex.org/C116219307","wikidata":"https://www.wikidata.org/wiki/Q7236625","display_name":"Power system simulation","level":4,"score":0.4918980598449707},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.317582905292511},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21397215127944946},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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":1,"locations":[{"id":"doi:10.1109/tsg.2017.2773603","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsg.2017.2773603","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","score":0.5199999809265137,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G7359251641","display_name":null,"funder_award_id":"PIOF-GA-2013-626014","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8098028047","display_name":null,"funder_award_id":"CCF-1442495","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"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W75577628","https://openalex.org/W806042187","https://openalex.org/W1555308066","https://openalex.org/W1858422019","https://openalex.org/W1966818217","https://openalex.org/W2000587848","https://openalex.org/W2007423841","https://openalex.org/W2015044695","https://openalex.org/W2020971083","https://openalex.org/W2039404136","https://openalex.org/W2051035766","https://openalex.org/W2072299359","https://openalex.org/W2094435766","https://openalex.org/W2286169807","https://openalex.org/W2296319761","https://openalex.org/W2397371338","https://openalex.org/W2572169820","https://openalex.org/W4250589301","https://openalex.org/W4256550092","https://openalex.org/W6623101297","https://openalex.org/W6695842710"],"related_works":["https://openalex.org/W1974955413","https://openalex.org/W2049251811","https://openalex.org/W2195904091","https://openalex.org/W2140602680","https://openalex.org/W2022218967","https://openalex.org/W2543208124","https://openalex.org/W1972673637","https://openalex.org/W4200353840","https://openalex.org/W2343483905","https://openalex.org/W2024013111"],"abstract_inverted_index":{"This":[0],"paper":[1,8],"is":[2,139,149],"Part":[3,35,49,89],"II":[4],"of":[5,29,112],"a":[6,11,45,69,96,124],"two-part":[7],"that":[9,53,72,118],"develops":[10],"multi-period":[12],"chance":[13],"constrained":[14],"optimal":[15],"power":[16],"flow":[17],"model":[18],"to":[19,62,67,110,154],"schedule":[20],"generation":[21],"and":[22,27,40,77,101,107,142],"reserves":[23],"from":[24],"both":[25],"generators":[26],"aggregations":[28],"uncertain":[30],"but":[31],"controllable":[32],"electric":[33],"loads.":[34],"I":[36],"developed":[37],"the":[38,42,64,85,93,103,113,119,133,155],"formulation":[39,71],"solved":[41,75,122],"problem":[43],"using":[44,123],"scenario-based":[46,86,114,134],"method.":[47,115,135],"In":[48],"II,":[50],"we":[51],"assume":[52],"all":[54],"uncertainties":[55],"follow":[56],"multivariate":[57],"normal":[58],"distributions,":[59],"allowing":[60],"us":[61],"reformulate":[63],"constraints":[65],"analytically":[66],"obtain":[68],"deterministic":[70],"can":[73],"be":[74],"faster":[76],"with":[78],"less":[79,129,140,143],"need":[80],"for":[81],"real":[82],"data":[83],"than":[84,132],"method":[87],"in":[88],"I.":[90],"We":[91,116],"test":[92],"approach":[94],"on":[95],"modified":[97],"IEEE":[98],"30-bus":[99],"system":[100],"compare":[102],"solutions,":[104],"empirical":[105,147],"reliabilities,":[106],"computational":[108,130],"requirements":[109],"those":[111],"find":[117],"analytical":[120],"reformulation":[121],"cutting":[125],"plane":[126],"algorithm":[127],"requires":[128],"time":[131],"Additionally,":[136],"its":[137,146],"solution":[138],"costly":[141],"conservative;":[144],"however,":[145],"reliability":[148],"lower,":[150],"though":[151],"still":[152],"close":[153],"desired":[156],"reliability.":[157]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":12}],"updated_date":"2026-03-28T08:17:26.163206","created_date":"2025-10-10T00:00:00"}
