{"id":"https://openalex.org/W7124239273","doi":"https://doi.org/10.3390/en19020426","title":"Optimal Operation of Distribution Networks Considering an Improved Voltage Stability Margin","display_name":"Optimal Operation of Distribution Networks Considering an Improved Voltage Stability Margin","publication_year":2026,"publication_date":"2026-01-15","ids":{"openalex":"https://openalex.org/W7124239273","doi":"https://doi.org/10.3390/en19020426"},"language":"en","primary_location":{"id":"doi:10.3390/en19020426","doi":"https://doi.org/10.3390/en19020426","is_oa":true,"landing_page_url":"https://doi.org/10.3390/en19020426","pdf_url":"https://www.mdpi.com/1996-1073/19/2/426/pdf","source":{"id":"https://openalex.org/S198098182","display_name":"Energies","issn_l":"1996-1073","issn":["1996-1073"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","norway-1","poland-140","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Energies","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1996-1073/19/2/426/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123058797","display_name":"Chen Dai","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen Dai","raw_affiliation_strings":["Electric Power Research Institute, State Grid Inner Mongolia Eastern Electric Power Co., Ltd., Hohhot 010020, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electric Power Research Institute, State Grid Inner Mongolia Eastern Electric Power Co., Ltd., Hohhot 010020, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123106266","display_name":"Sitong Yan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sitong Yan","raw_affiliation_strings":["Electric Power Research Institute, State Grid Inner Mongolia Eastern Electric Power Co., Ltd., Hohhot 010020, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electric Power Research Institute, State Grid Inner Mongolia Eastern Electric Power Co., Ltd., Hohhot 010020, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042248392","display_name":"Chuang Yu","orcid":"https://orcid.org/0000-0003-2604-4282","observed_orcids":["https://orcid.org/0000-0003-2604-4282","https://orcid.org/0000-0003-3185-3578","https://orcid.org/0009-0009-3219-6961"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chuang Yu","raw_affiliation_strings":["Electric Power Research Institute, State Grid Inner Mongolia Eastern Electric Power Co., Ltd., Hohhot 010020, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electric Power Research Institute, State Grid Inner Mongolia Eastern Electric Power Co., Ltd., Hohhot 010020, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Xiufeng Wang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiufeng Wang","raw_affiliation_strings":["Electric Power Research Institute, State Grid Inner Mongolia Eastern Electric Power Co., Ltd., Hohhot 010020, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electric Power Research Institute, State Grid Inner Mongolia Eastern Electric Power Co., Ltd., Hohhot 010020, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063366252","display_name":"Q. Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qianran Zhang","raw_affiliation_strings":["Electric Power Research Institute, State Grid Inner Mongolia Eastern Electric Power Co., Ltd., Hohhot 010020, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electric Power Research Institute, State Grid Inner Mongolia Eastern Electric Power Co., Ltd., Hohhot 010020, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123166364","display_name":"Lichao Zhou","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lichao Zhou","raw_affiliation_strings":["Electric Power Research Institute, State Grid Inner Mongolia Eastern Electric Power Co., Ltd., Hohhot 010020, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electric Power Research Institute, State Grid Inner Mongolia Eastern Electric Power Co., Ltd., Hohhot 010020, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021947260","display_name":"Zifa Liu","orcid":"https://orcid.org/0000-0003-3225-4040","observed_orcids":["https://orcid.org/0000-0003-3225-4040","https://orcid.org/0000-0003-3236-1460","https://orcid.org/0000-0002-9805-698X","https://orcid.org/0000-0002-6407-9008"]},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zifa Liu","raw_affiliation_strings":["School of Electrical and Electronic Engineering, North China Electric Power University, Changping District, Beijing 102206, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, North China Electric Power University, Changping District, Beijing 102206, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123142236","display_name":"Ming Gong","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ming Gong","raw_affiliation_strings":["School of Electrical and Electronic Engineering, North China Electric Power University, Changping District, Beijing 102206, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, North China Electric Power University, Changping District, Beijing 102206, China","institution_ids":["https://openalex.org/I153473198"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5123142236"],"corresponding_institution_ids":["https://openalex.org/I153473198"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02211885,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"2","first_page":"426","last_page":"426"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.9848999977111816,"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":0.9848999977111816,"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/T10424","display_name":"Electric Power System Optimization","score":0.010400000028312206,"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":0.002099999925121665,"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/voltage-stability-margin","display_name":"voltage stability margin","score":0.8849999904632568},{"id":"https://openalex.org/keywords/voltage-instability","display_name":"voltage instability","score":0.6930000185966492},{"id":"https://openalex.org/keywords/renewable-energy-penetration","display_name":"renewable energy penetration","score":0.6859999895095825},{"id":"https://openalex.org/keywords/distributed-generation","display_name":"distributed generation","score":0.8289999961853027},{"id":"https://openalex.org/keywords/multi-objective-scheduling","display_name":"multi-objective scheduling","score":0.7580000162124634},{"id":"https://openalex.org/keywords/mixed-integer-programming","display_name":"mixed integer programming","score":0.7149999737739563},{"id":"https://openalex.org/keywords/energy-storage","display_name":"energy storage","score":0.6800000071525574},{"id":"https://openalex.org/keywords/epsilon-constraint-method","display_name":"epsilon-constraint method","score":0.7379999756813049},{"id":"https://openalex.org/keywords/pareto-front","display_name":"Pareto front","score":0.7979999780654907},{"id":"https://openalex.org/keywords/electricity-purchase-cost","display_name":"electricity purchase cost","score":0.921999990940094}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5629000067710876},{"id":"https://openalex.org/C544738498","wikidata":"https://www.wikidata.org/wiki/Q861135","display_name":"Distributed generation","level":3,"score":0.5318999886512756},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49570000171661377},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.47690001130104065},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4472000002861023},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.43549999594688416},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.4350000023841858},{"id":"https://openalex.org/C188573790","wikidata":"https://www.wikidata.org/wiki/Q12705","display_name":"Renewable energy","level":2,"score":0.4318000078201294},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.39579999446868896},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.3935000002384186},{"id":"https://openalex.org/C17829176","wikidata":"https://www.wikidata.org/wiki/Q179043","display_name":"Electrical impedance","level":2,"score":0.3495999872684479},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.32760000228881836},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3231000006198883},{"id":"https://openalex.org/C206658404","wikidata":"https://www.wikidata.org/wiki/Q12725","display_name":"Electricity","level":2,"score":0.310699999332428},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2937000095844269},{"id":"https://openalex.org/C108755667","wikidata":"https://www.wikidata.org/wiki/Q1930258","display_name":"AC power","level":3,"score":0.28949999809265137},{"id":"https://openalex.org/C423512","wikidata":"https://www.wikidata.org/wiki/Q383973","display_name":"Electricity generation","level":3,"score":0.28630000352859497},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C196226539","wikidata":"https://www.wikidata.org/wiki/Q7940752","display_name":"Voltage regulation","level":3,"score":0.2773999869823456},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.27309998869895935},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C206888370","wikidata":"https://www.wikidata.org/wiki/Q844861","display_name":"Electric power distribution","level":3,"score":0.2605000138282776},{"id":"https://openalex.org/C2780165032","wikidata":"https://www.wikidata.org/wiki/Q16869822","display_name":"Energy consumption","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C104122410","wikidata":"https://www.wikidata.org/wiki/Q1416406","display_name":"Network model","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C73916439","wikidata":"https://www.wikidata.org/wiki/Q837718","display_name":"Energy storage","level":3,"score":0.2556999921798706},{"id":"https://openalex.org/C128624480","wikidata":"https://www.wikidata.org/wiki/Q1504817","display_name":"Low voltage","level":3,"score":0.2517000138759613},{"id":"https://openalex.org/C2775896111","wikidata":"https://www.wikidata.org/wiki/Q642560","display_name":"Router","level":2,"score":0.2517000138759613},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/en19020426","doi":"https://doi.org/10.3390/en19020426","is_oa":true,"landing_page_url":"https://doi.org/10.3390/en19020426","pdf_url":"https://www.mdpi.com/1996-1073/19/2/426/pdf","source":{"id":"https://openalex.org/S198098182","display_name":"Energies","issn_l":"1996-1073","issn":["1996-1073"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","norway-1","poland-140","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Energies","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:2542957035dc4098967fe059990a94b5","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/2542957035dc4098967fe059990a94b5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Energies, Vol 19, Iss 2, p 426 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/en19020426","doi":"https://doi.org/10.3390/en19020426","is_oa":true,"landing_page_url":"https://doi.org/10.3390/en19020426","pdf_url":"https://www.mdpi.com/1996-1073/19/2/426/pdf","source":{"id":"https://openalex.org/S198098182","display_name":"Energies","issn_l":"1996-1073","issn":["1996-1073"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","norway-1","poland-140","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Energies","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":1.0,"display_name":"Industry, innovation and infrastructure"},{"id":"https://metadata.un.org/sdg/7","score":0.9853000044822693,"display_name":"Affordable and clean energy"}],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/7","score":0.8397839069366455,"display_name":"Affordable and clean energy"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7124239273.pdf","grobid_xml":"https://content.openalex.org/works/W7124239273.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1997049313","https://openalex.org/W2559956088","https://openalex.org/W2765842113","https://openalex.org/W2783740032","https://openalex.org/W2910844709","https://openalex.org/W4206776063","https://openalex.org/W4407253556"],"related_works":[],"abstract_inverted_index":{"To":[0],"address":[1],"the":[2,50,62,66,70,76,82,89,109,124,128,139,149,170,175,181,185,190,194,209,213,218,230],"voltage":[3,27,186],"instability":[4],"in":[5,81,229],"distribution":[6,38,85,214,219,231],"networks":[7,39],"with":[8,108],"a":[9,15,153,203,222],"high":[10,223],"penetration":[11],"of":[12,54,65,75,92,127,131,169,189,197,212,225],"renewable":[13],"energy,":[14],"multi-objective":[16,102],"optimal":[17,210],"scheduling":[18],"method":[19,177,207],"is":[20,40,106,136,158],"proposed":[21,176],"based":[22],"on":[23,61,148],"an":[24],"enhanced":[25],"static":[26],"stability":[28,145,187],"margin":[29,188],"ratio":[30],"(SVSMR).":[31],"The":[32,167],"SVSMRd":[33,77,129],"index":[34,78,130],"suitable":[35],"for":[36,208],"complex":[37],"constructed":[41],"by":[42],"analytical":[43],"derivation":[44],"and":[45,49,72,88,94,119,123,192,206,216],"equivalent":[46],"impedance":[47],"correction,":[48],"distributed":[51,55],"access":[52,228],"characteristics":[53],"power":[56],"generation":[57],"are":[58,79,96],"considered.":[59],"Based":[60,147],"simulation":[63,68],"analysis":[64,172],"PS_CAD":[67],"platform,":[69],"effectiveness":[71],"engineering":[73],"applicability":[74],"compared":[80],"multi-energy":[83],"station":[84],"network":[86,116,220],"scenario,":[87],"calculation":[90],"results":[91,168],"SVSMRF":[93],"SDSCR":[95],"used":[97,137],"to":[98,142],"verify":[99],"it.":[100],"A":[101],"mixed-integer":[103],"optimisation":[104,140,196],"model":[105],"constructed,":[107],"objective":[110],"function":[111],"encompassing":[112],"electricity":[113],"purchase":[114],"cost,":[115,118,183],"loss":[117],"energy":[120,134,227],"storage":[121],"revenue,":[122],"lowest":[125],"value":[126],"various":[132],"new":[133,204,226],"nodes":[135],"as":[138],"object":[141],"carry":[143],"out":[144],"targets.":[146],"epsilon":[150],"constraint":[151],"method,":[152],"Pareto":[154],"frontier":[155],"solution":[156],"set":[157],"generated":[159],"through":[160],"example":[161,171],"analysis,":[162],"which":[163],"has":[164],"non-dominant":[165],"characteristics.":[166],"show":[173],"that":[174],"can":[178],"effectively":[179],"reduce":[180],"operating":[182],"ensure":[184],"system,":[191],"realise":[193],"collaborative":[195],"source\u2013network\u2013load\u2013storage":[198],"resources.":[199],"This":[200],"paper":[201],"provides":[202],"idea":[205],"operation":[211],"network,":[215],"optimises":[217],"under":[221],"proportion":[224],"network.":[232]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2026-01-16T00:00:00"}