{"id":"https://openalex.org/W2583928650","doi":"https://doi.org/10.1109/globalsip.2016.7905963","title":"Convergence of the Z-Bus method and existence of unique solution in single-phase distribution load-flow","display_name":"Convergence of the Z-Bus method and existence of unique solution in single-phase distribution load-flow","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2583928650","doi":"https://doi.org/10.1109/globalsip.2016.7905963","mag":"2583928650"},"language":"en","primary_location":{"id":"doi:10.1109/globalsip.2016.7905963","is_oa":false,"landing_page_url":"https://doi.org/10.1109/globalsip.2016.7905963","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP)","raw_type":"proceedings-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/A5041359038","display_name":"Mohammadhafez Bazrafshan","orcid":"https://orcid.org/0000-0002-1331-1321"},"institutions":[{"id":"https://openalex.org/I45438204","display_name":"The University of Texas at San Antonio","ror":"https://ror.org/01kd65564","country_code":"US","type":"education","lineage":["https://openalex.org/I45438204"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mohammadhafez Bazrafshan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, The University of Texas at San Antonio"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, The University of Texas at San Antonio","institution_ids":["https://openalex.org/I45438204"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022494957","display_name":"Nikolaos Gatsis","orcid":"https://orcid.org/0000-0002-5238-649X"},"institutions":[{"id":"https://openalex.org/I45438204","display_name":"The University of Texas at San Antonio","ror":"https://ror.org/01kd65564","country_code":"US","type":"education","lineage":["https://openalex.org/I45438204"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nikolaos Gatsis","raw_affiliation_strings":["Department of Electrical and Computer Engineering, The University of Texas at San Antonio"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, The University of Texas at San Antonio","institution_ids":["https://openalex.org/I45438204"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041359038"],"corresponding_institution_ids":["https://openalex.org/I45438204"],"apc_list":null,"apc_paid":null,"fwci":0.5593,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.73121042,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"851","last_page":"855"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9988999962806702,"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/T10603","display_name":"Smart Grid Energy Management","score":0.9987000226974487,"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/initialization","display_name":"Initialization","score":0.7868516445159912},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6549395322799683},{"id":"https://openalex.org/keywords/electrical-impedance","display_name":"Electrical impedance","score":0.6200708746910095},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6159944534301758},{"id":"https://openalex.org/keywords/power-flow","display_name":"Power flow","score":0.5532504916191101},{"id":"https://openalex.org/keywords/constant-current","display_name":"Constant current","score":0.5121955275535583},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.506421685218811},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4854641556739807},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4328835606575012},{"id":"https://openalex.org/keywords/three-phase","display_name":"Three-phase","score":0.43054574728012085},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42384809255599976},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4004301428794861},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.39075008034706116},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3777625560760498},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35040032863616943},{"id":"https://openalex.org/keywords/current","display_name":"Current (fluid)","score":0.33934682607650757},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32874995470046997},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.29251617193222046},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.21706250309944153},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.1662757396697998},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15566256642341614},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.15513983368873596},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14058899879455566}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.7868516445159912},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6549395322799683},{"id":"https://openalex.org/C17829176","wikidata":"https://www.wikidata.org/wiki/Q179043","display_name":"Electrical impedance","level":2,"score":0.6200708746910095},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6159944534301758},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.5532504916191101},{"id":"https://openalex.org/C53392680","wikidata":"https://www.wikidata.org/wiki/Q5163647","display_name":"Constant current","level":3,"score":0.5121955275535583},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.506421685218811},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4854641556739807},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4328835606575012},{"id":"https://openalex.org/C173871940","wikidata":"https://www.wikidata.org/wiki/Q471846","display_name":"Three-phase","level":3,"score":0.43054574728012085},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42384809255599976},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4004301428794861},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.39075008034706116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3777625560760498},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35040032863616943},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.33934682607650757},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32874995470046997},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.29251617193222046},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.21706250309944153},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.1662757396697998},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15566256642341614},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.15513983368873596},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14058899879455566},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/globalsip.2016.7905963","is_oa":false,"landing_page_url":"https://doi.org/10.1109/globalsip.2016.7905963","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1507082306","https://openalex.org/W1603765807","https://openalex.org/W1901949613","https://openalex.org/W1984452440","https://openalex.org/W2031454011","https://openalex.org/W2184525671","https://openalex.org/W2962977694","https://openalex.org/W2963059498","https://openalex.org/W2963469565","https://openalex.org/W4236451413"],"related_works":["https://openalex.org/W3204184292","https://openalex.org/W3176564347","https://openalex.org/W1985458517","https://openalex.org/W2355833770","https://openalex.org/W3031039437","https://openalex.org/W183202219","https://openalex.org/W3095877357","https://openalex.org/W2072565696","https://openalex.org/W2050451745","https://openalex.org/W2364081541"],"abstract_inverted_index":{"For":[0],"a":[1,20,23,35],"single-phase":[2],"distribution":[3,68],"network":[4],"with":[5],"constant-power,":[6],"constant-current,":[7],"and":[8],"constant-impedance":[9],"loads":[10],"(ZIP":[11],"loads),":[12],"sufficient":[13,55],"conditions":[14,56],"are":[15,63],"presented":[16],"that":[17],"explicitly":[18],"define":[19],"region":[21],"where":[22],"unique":[24,51],"load-flow":[25,52],"solution":[26],"exists.":[27],"The":[28,54],"Z-Bus":[29,61],"method":[30,62],"is":[31,45],"shown":[32],"to":[33,47,49],"be":[34],"contraction":[36],"mapping":[37],"iteration,":[38],"which":[39],"upon":[40],"initialization":[41],"within":[42],"this":[43],"region,":[44],"guaranteed":[46],"converge":[48],"the":[50,60],"solution.":[53],"for":[57,66],"convergence":[58],"of":[59],"numerically":[64],"verified":[65],"IEEE":[67],"test":[69],"feeders.":[70]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}