{"id":"https://openalex.org/W7204490688","doi":"https://doi.org/10.3390/en19174025","title":"Voltage Stability Assessment in Modern Power Systems: A Structured Review of Methods and Indices","display_name":"Voltage Stability Assessment in Modern Power Systems: A Structured Review of Methods and Indices","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204490688","doi":"https://doi.org/10.3390/en19174025"},"language":"en","primary_location":{"id":"doi:10.3390/en19174025","doi":"https://doi.org/10.3390/en19174025","is_oa":true,"landing_page_url":"https://doi.org/10.3390/en19174025","pdf_url":null,"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","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/en19174025","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013549141","display_name":"Annalisa Liccardo","orcid":"https://orcid.org/0000-0003-1270-4948","observed_orcids":["https://orcid.org/0000-0003-1270-4948"]},"institutions":[{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Annalisa Liccardo","raw_affiliation_strings":["Department of Electrical Engineering and Information Technology, University of Naples Federico II, 80125 Naples, Italy"],"raw_orcid":"https://orcid.org/0000-0003-1270-4948","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Information Technology, University of Naples Federico II, 80125 Naples, Italy","institution_ids":["https://openalex.org/I71267560"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035788028","display_name":"Davide Lauria","orcid":"https://orcid.org/0000-0003-4579-0440","observed_orcids":["https://orcid.org/0000-0003-4579-0440"]},"institutions":[{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Davide Lauria","raw_affiliation_strings":["Department of Industrial Engineering, University of Naples Federico II, 80125 Naples, Italy"],"raw_orcid":"https://orcid.org/0000-0003-4579-0440","affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, University of Naples Federico II, 80125 Naples, Italy","institution_ids":["https://openalex.org/I71267560"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075309288","display_name":"Francesco Bonavolont\u00e0","orcid":"https://orcid.org/0000-0003-0666-0942","observed_orcids":["https://orcid.org/0000-0003-0666-0942"]},"institutions":[{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Bonavolont\u00e0","raw_affiliation_strings":["Department of Electrical Engineering and Information Technology, University of Naples Federico II, 80125 Naples, Italy"],"raw_orcid":"https://orcid.org/0000-0003-0666-0942","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Information Technology, University of Naples Federico II, 80125 Naples, Italy","institution_ids":["https://openalex.org/I71267560"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062181802","display_name":"Guido Coletta","orcid":"https://orcid.org/0000-0002-9125-4334","observed_orcids":["https://orcid.org/0000-0002-9125-4334"]},"institutions":[{"id":"https://openalex.org/I4210101959","display_name":"Terna (Italy)","ror":"https://ror.org/013nb7b55","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210101959"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Guido Coletta","raw_affiliation_strings":["Terna S.p.A., 00156 Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9125-4334","affiliations":[{"raw_affiliation_string":"Terna S.p.A., 00156 Rome, Italy","institution_ids":["https://openalex.org/I4210101959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032993563","display_name":"Giorgio Maria Giannuzzi","orcid":"https://orcid.org/0000-0003-0314-4483","observed_orcids":["https://orcid.org/0000-0003-0314-4483"]},"institutions":[{"id":"https://openalex.org/I4210101959","display_name":"Terna (Italy)","ror":"https://ror.org/013nb7b55","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210101959"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giorgio Maria Giannuzzi","raw_affiliation_strings":["Terna S.p.A., 00156 Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Terna S.p.A., 00156 Rome, Italy","institution_ids":["https://openalex.org/I4210101959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063939133","display_name":"Salvatore Tessitore","orcid":"https://orcid.org/0000-0002-3674-9211","observed_orcids":["https://orcid.org/0000-0002-3674-9211"]},"institutions":[{"id":"https://openalex.org/I4210101959","display_name":"Terna (Italy)","ror":"https://ror.org/013nb7b55","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210101959"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Salvatore Tessitore","raw_affiliation_strings":["Terna S.p.A., 00156 Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Terna S.p.A., 00156 Rome, Italy","institution_ids":["https://openalex.org/I4210101959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016540881","display_name":"Cosimo Pisani","orcid":"https://orcid.org/0000-0003-2964-9025","observed_orcids":["https://orcid.org/0000-0003-2964-9025"]},"institutions":[{"id":"https://openalex.org/I4210101959","display_name":"Terna (Italy)","ror":"https://ror.org/013nb7b55","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210101959"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Cosimo Pisani","raw_affiliation_strings":["Terna S.p.A., 00156 Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0003-2964-9025","affiliations":[{"raw_affiliation_string":"Terna S.p.A., 00156 Rome, Italy","institution_ids":["https://openalex.org/I4210101959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013549141"],"corresponding_institution_ids":["https://openalex.org/I71267560"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":2.6739,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.86645622,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"19","issue":"17","first_page":"4025","last_page":"4025"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10305","display_name":"Power System Optimization and Stability","score":1.0,"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/T10305","display_name":"Power System Optimization and Stability","score":1.0,"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/T11941","display_name":"Power System Reliability and Maintenance","score":0.0,"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/T10454","display_name":"Optimal Power Flow Distribution","score":0.0,"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-assessment","display_name":"voltage stability assessment","score":0.9679999947547913},{"id":"https://openalex.org/keywords/voltage-stability-index","display_name":"voltage stability index","score":0.9380000233650208},{"id":"https://openalex.org/keywords/inverter-based-resources","display_name":"inverter-based resources","score":0.8610000014305115},{"id":"https://openalex.org/keywords/l-index","display_name":"L-index","score":0.5389999747276306},{"id":"https://openalex.org/keywords/lyapunov-exponents","display_name":"Lyapunov exponents","score":0.9620000123977661},{"id":"https://openalex.org/keywords/wide-area-monitoring","display_name":"wide-area monitoring","score":0.8939999938011169},{"id":"https://openalex.org/keywords/threshold-definition","display_name":"threshold definition","score":0.7239999771118164}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5853000283241272},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.5723999738693237},{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.5590999722480774},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.5134999752044678},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.507099986076355},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4171000123023987},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.38909998536109924},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.388700008392334},{"id":"https://openalex.org/C92018576","wikidata":"https://www.wikidata.org/wiki/Q3242194","display_name":"Power transmission","level":3,"score":0.3837999999523163},{"id":"https://openalex.org/C2983254600","wikidata":"https://www.wikidata.org/wiki/Q1096907","display_name":"Power grid","level":3,"score":0.37040001153945923},{"id":"https://openalex.org/C177454536","wikidata":"https://www.wikidata.org/wiki/Q578290","display_name":"Emphasis (telecommunications)","level":2,"score":0.3675000071525574},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3506999909877777},{"id":"https://openalex.org/C196226539","wikidata":"https://www.wikidata.org/wiki/Q7940752","display_name":"Voltage regulation","level":3,"score":0.32710000872612},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C46529443","wikidata":"https://www.wikidata.org/wiki/Q7940750","display_name":"Voltage optimisation","level":4,"score":0.31139999628067017},{"id":"https://openalex.org/C2779553522","wikidata":"https://www.wikidata.org/wiki/Q15261121","display_name":"National Grid","level":3,"score":0.3066999912261963},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.29260000586509705},{"id":"https://openalex.org/C113608303","wikidata":"https://www.wikidata.org/wiki/Q1056835","display_name":"Transmission system","level":3,"score":0.29100000858306885},{"id":"https://openalex.org/C10558101","wikidata":"https://www.wikidata.org/wiki/Q689855","display_name":"Smart grid","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C108755667","wikidata":"https://www.wikidata.org/wiki/Q1930258","display_name":"AC power","level":3,"score":0.26809999346733093},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.2572999894618988}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/en19174025","doi":"https://doi.org/10.3390/en19174025","is_oa":true,"landing_page_url":"https://doi.org/10.3390/en19174025","pdf_url":null,"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:d53aca640c004ebbb1afe9471de5b96a","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/d53aca640c004ebbb1afe9471de5b96a","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Energies, Vol 19, Iss 17, p 4025 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/en19174025","doi":"https://doi.org/10.3390/en19174025","is_oa":true,"landing_page_url":"https://doi.org/10.3390/en19174025","pdf_url":null,"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":[{"display_name":"Industry, innovation and infrastructure","score":0.8970999717712402,"id":"https://metadata.un.org/sdg/9"},{"display_name":"Affordable and clean energy","score":0.8485000133514404,"id":"https://metadata.un.org/sdg/7"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W2102131743","https://openalex.org/W2109680636","https://openalex.org/W2129138344","https://openalex.org/W2146687065","https://openalex.org/W2148213050","https://openalex.org/W2173341126","https://openalex.org/W2290543666","https://openalex.org/W2291017068","https://openalex.org/W2323703042","https://openalex.org/W2418469734","https://openalex.org/W2419626787","https://openalex.org/W2541620444","https://openalex.org/W2593547385","https://openalex.org/W2603193289","https://openalex.org/W2766763729","https://openalex.org/W2769530609","https://openalex.org/W2921837127","https://openalex.org/W2961957032","https://openalex.org/W3036098369","https://openalex.org/W3095971614","https://openalex.org/W3101482998","https://openalex.org/W3110874572","https://openalex.org/W3129175333","https://openalex.org/W3129363353","https://openalex.org/W3134071777","https://openalex.org/W3163516067","https://openalex.org/W3166539331","https://openalex.org/W3177710071","https://openalex.org/W3209872041","https://openalex.org/W3213107319","https://openalex.org/W4206587460","https://openalex.org/W4212821273","https://openalex.org/W4285248540","https://openalex.org/W4311724006","https://openalex.org/W4315694840","https://openalex.org/W4400003298","https://openalex.org/W4408017318","https://openalex.org/W4408384007","https://openalex.org/W4411271774"],"related_works":["https://openalex.org/W3110162658","https://openalex.org/W3177710071","https://openalex.org/W2539806620","https://openalex.org/W4388294132","https://openalex.org/W4214504196","https://openalex.org/W2901886262","https://openalex.org/W2056859172","https://openalex.org/W3014937411","https://openalex.org/W4206988318","https://openalex.org/W1904089337"],"abstract_inverted_index":{"The":[0,53,95],"increasing":[1],"penetration":[2],"of":[3,10,22,31,149],"inverter-based":[4],"resources":[5],"and":[6,35,50,58,67,74,88,113,124,146],"the":[7,32,82,133,147],"growing":[8],"complexity":[9],"modern":[11],"power":[12,130],"systems":[13],"have":[14],"made":[15],"voltage":[16,39,60,106],"stability":[17,40,61,154],"assessment":[18,155],"a":[19,29,117],"critical":[20],"aspect":[21],"transmission":[23],"network":[24],"operation.":[25],"This":[26],"paper":[27],"presents":[28],"review":[30,54],"main":[33,83,134],"methods":[34],"indices":[36,115],"adopted":[37],"for":[38,90,121],"assessment,":[41],"with":[42],"emphasis":[43],"on":[44],"their":[45],"applicability":[46],"to":[47,138],"real-time":[48,125],"monitoring":[49,92,123],"inverter-dominated":[51],"grids.":[52],"covers":[55],"both":[56],"long-term":[57],"short-term":[59],"approaches,":[62],"including":[63],"L-index":[64],"methods,":[65,71],"Jacobian-":[66],"singular-value-based":[68],"techniques,":[69],"Lyapunov-exponent-based":[70],"trajectory-based":[72],"indices,":[73],"recent":[75],"artificial":[76],"intelligence":[77],"applications.":[78],"For":[79],"each":[80],"method,":[81],"advantages,":[84],"limitations,":[85],"computational":[86],"requirements,":[87],"suitability":[89],"PMU-based":[91],"are":[93,157],"discussed.":[94,158],"analysis":[96],"shows":[97],"that":[98],"no":[99],"single":[100],"indicator":[101],"can":[102],"fully":[103],"describe":[104],"all":[105],"instability":[107],"phenomena.":[108],"Instead,":[109],"combining":[110],"complementary":[111],"static":[112],"dynamic":[114],"provides":[116],"more":[118],"complete":[119],"basis":[120],"wide-area":[122],"operational":[126,153],"support":[127],"in":[128],"future":[129],"systems.":[131],"Moreover,":[132],"open":[135],"challenges":[136],"related":[137],"threshold":[139],"definition,":[140],"robustness":[141],"under":[142],"evolving":[143],"grid":[144],"conditions,":[145],"integration":[148],"data-driven":[150],"techniques":[151],"into":[152],"schemes":[156]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-08-28T00:00:00"}