{"id":"https://openalex.org/W2785637931","doi":"https://doi.org/10.1109/tim.2017.2782980","title":"Maximum Likelihood Parameter Estimation of Unbalanced Three-Phase Power Signals","display_name":"Maximum Likelihood Parameter Estimation of Unbalanced Three-Phase Power Signals","publication_year":2018,"publication_date":"2018-01-18","ids":{"openalex":"https://openalex.org/W2785637931","doi":"https://doi.org/10.1109/tim.2017.2782980","mag":"2785637931"},"language":"en","primary_location":{"id":"doi:10.1109/tim.2017.2782980","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2017.2782980","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"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 Instrumentation and Measurement","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/A5005242197","display_name":"Yili Xia","orcid":"https://orcid.org/0000-0002-4402-8131"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yili Xia","raw_affiliation_strings":["School of Information Science and Engineering, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-4402-8131","affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076106664","display_name":"Sithan Kanna","orcid":"https://orcid.org/0000-0001-5714-461X"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Sithan Kanna","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, London, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, U.K","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103001848","display_name":"Danilo P. Mandic","orcid":"https://orcid.org/0000-0001-8432-3963"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Danilo P. Mandic","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, London, U.K"],"raw_orcid":"https://orcid.org/0000-0001-8432-3963","affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, U.K","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005242197"],"corresponding_institution_ids":["https://openalex.org/I76569877"],"apc_list":null,"apc_paid":null,"fwci":3.403,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.92867764,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"67","issue":"3","first_page":"569","last_page":"581"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10573","display_name":"Power Quality and Harmonics","score":0.9998999834060669,"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/T10573","display_name":"Power Quality and Harmonics","score":0.9998999834060669,"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":0.9991000294685364,"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/T10223","display_name":"Microgrid Control and Optimization","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.7660453915596008},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6889472603797913},{"id":"https://openalex.org/keywords/maximum-likelihood-sequence-estimation","display_name":"Maximum likelihood sequence estimation","score":0.5510474443435669},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.5357664227485657},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4952923357486725},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.4944171905517578},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.49030569195747375},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4787710905075073},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4752856492996216},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.4688986837863922},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4423995912075043},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4419056177139282},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.42624765634536743},{"id":"https://openalex.org/keywords/three-phase","display_name":"Three-phase","score":0.4187565743923187},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.41631919145584106},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3943362534046173},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.3902750015258789},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3601738512516022},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.30753064155578613},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.28973835706710815},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.13724854588508606},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.13355451822280884}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.7660453915596008},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6889472603797913},{"id":"https://openalex.org/C191462741","wikidata":"https://www.wikidata.org/wiki/Q6795902","display_name":"Maximum likelihood sequence estimation","level":3,"score":0.5510474443435669},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.5357664227485657},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4952923357486725},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.4944171905517578},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.49030569195747375},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4787710905075073},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4752856492996216},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.4688986837863922},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4423995912075043},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4419056177139282},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.42624765634536743},{"id":"https://openalex.org/C173871940","wikidata":"https://www.wikidata.org/wiki/Q471846","display_name":"Three-phase","level":3,"score":0.4187565743923187},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.41631919145584106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3943362534046173},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3902750015258789},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3601738512516022},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.30753064155578613},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.28973835706710815},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.13724854588508606},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.13355451822280884},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tim.2017.2782980","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2017.2782980","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"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 Instrumentation and Measurement","raw_type":"journal-article"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/58182","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/58182","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"581","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6200000047683716,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G1256811535","display_name":null,"funder_award_id":"2242016K41050","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3589703592","display_name":null,"funder_award_id":"61401094","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7616653276","display_name":null,"funder_award_id":"BK20140645","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G8335968205","display_name":null,"funder_award_id":"61771124","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320283","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W142384176","https://openalex.org/W250076511","https://openalex.org/W655409003","https://openalex.org/W1500762955","https://openalex.org/W1506809288","https://openalex.org/W1965041626","https://openalex.org/W1967672332","https://openalex.org/W1973717650","https://openalex.org/W1980072023","https://openalex.org/W1980889830","https://openalex.org/W1982785656","https://openalex.org/W1997237426","https://openalex.org/W1998345848","https://openalex.org/W2001188690","https://openalex.org/W2005262499","https://openalex.org/W2023993834","https://openalex.org/W2027115776","https://openalex.org/W2042663762","https://openalex.org/W2043436843","https://openalex.org/W2048584642","https://openalex.org/W2061100755","https://openalex.org/W2067489830","https://openalex.org/W2069915610","https://openalex.org/W2075443350","https://openalex.org/W2098782404","https://openalex.org/W2100567194","https://openalex.org/W2103457274","https://openalex.org/W2107237980","https://openalex.org/W2110711675","https://openalex.org/W2112106839","https://openalex.org/W2113072220","https://openalex.org/W2114528197","https://openalex.org/W2115577730","https://openalex.org/W2119280775","https://openalex.org/W2119472435","https://openalex.org/W2121499406","https://openalex.org/W2126435449","https://openalex.org/W2126960233","https://openalex.org/W2127300534","https://openalex.org/W2129241503","https://openalex.org/W2129842740","https://openalex.org/W2130059336","https://openalex.org/W2130358341","https://openalex.org/W2137019349","https://openalex.org/W2139424477","https://openalex.org/W2140717263","https://openalex.org/W2140870634","https://openalex.org/W2150765859","https://openalex.org/W2151107605","https://openalex.org/W2153785453","https://openalex.org/W2155833003","https://openalex.org/W2160525803","https://openalex.org/W2161859765","https://openalex.org/W2168259461","https://openalex.org/W2169190201","https://openalex.org/W2169371741","https://openalex.org/W2193986013","https://openalex.org/W2326590224","https://openalex.org/W2344251239","https://openalex.org/W2463127997","https://openalex.org/W2466582317","https://openalex.org/W2476841360","https://openalex.org/W2562386792","https://openalex.org/W2593628325","https://openalex.org/W2661279125","https://openalex.org/W4232254893","https://openalex.org/W4245365756"],"related_works":["https://openalex.org/W2366184732","https://openalex.org/W1499442185","https://openalex.org/W2379466508","https://openalex.org/W1573889165","https://openalex.org/W2392411825","https://openalex.org/W1559074081","https://openalex.org/W3023909498","https://openalex.org/W2808306767","https://openalex.org/W1503532423","https://openalex.org/W2120595071"],"abstract_inverted_index":{"Accurate":[0],"detection":[1],"of":[2,20,30,82,136,140,175],"the":[3,15,46,58,68,97,102,110,134,142,149,158,176,197],"system":[4,187],"parameters":[5,205],"in":[6],"unbalanced":[7,34,60,106,184],"three-phase":[8,185],"power":[9,186],"systems":[10,35],"is":[11,77,91,116,121,168],"a":[12,80,124,165],"prerequisite":[13],"for":[14,33,53,66,74,95,203],"optimal":[16],"operation":[17],"and":[18,26,118,138,144,178],"control":[19],"future":[21],"smart":[22],"grids.":[23],"However,":[24],"theoretical":[25,201],"practical":[27],"performance":[28],"bounds":[29,51],"various":[31],"estimators":[32],"are":[36],"only":[37],"just":[38],"being":[39],"established.":[40],"To":[41,108],"this":[42,163],"end,":[43],"we":[44],"introduce":[45],"appropriate":[47],"Cramer-":[48],"Rao":[49],"lower":[50],"(CRLBs)":[52],"frequency":[54,75,160,190],"estimation,":[55],"based":[56,156],"on":[57,157],"\u03b1\u03b2-transformed":[59,150],"voltage":[61,151,173],"contaminated":[62],"with":[63,105],"noise.":[64],"Next,":[65],"rigor,":[67],"maximum":[69],"likelihood":[70],"estimation":[71,76],"(MLE)":[72],"method":[73,115],"introduced":[78],"as":[79],"maximizer":[81],"an":[83,183],"\u201caugmented":[84],"periodogram.\u201d":[85],"The":[86],"underlying":[87],"augmented":[88],"complex":[89],"statistics":[90],"shown":[92],"to":[93,170],"cater":[94],"all":[96,204],"available":[98],"secondorder":[99],"information,":[100],"including":[101],"noncircularity":[103],"associated":[104],"systems.":[107],"find":[109],"ML":[111,159],"solution,":[112],"Newton's":[113],"iterative":[114],"employed":[117],"its":[119,189],"initialization":[120],"implemented":[122],"by":[123],"discrete":[125],"Fourier":[126],"transform-based":[127],"dichotomous":[128],"search":[129],"technique.":[130],"We":[131],"show":[132],"that":[133,196],"MLE":[135,199],"phases":[137],"amplitudes":[139],"both":[141],"positive":[143,177],"negative":[145,179],"phase-sequence":[146,180],"components":[147,181],"within":[148,182],"can":[152],"be":[153],"generically":[154],"derived":[155],"estimates.":[161],"In":[162],"way,":[164],"unified":[166],"framework":[167],"provided":[169],"accurately":[171],"detect":[172],"characteristics":[174],"when":[188],"experiences":[191],"off-nominal":[192],"conditions.":[193],"Simulations":[194],"verify":[195],"proposed":[198],"approaches":[200],"CRLBs":[202],"under":[206],"consideration.":[207]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
