{"id":"https://openalex.org/W4415913622","doi":"https://doi.org/10.1109/tpwrs.2026.3741483","title":"Quantifying Grid-Forming Behavior: Bridging Device-Level Dynamics and System-Level Strength","display_name":"Quantifying Grid-Forming Behavior: Bridging Device-Level Dynamics and System-Level Strength","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W4415913622","doi":"https://doi.org/10.1109/tpwrs.2026.3741483"},"language":"en","primary_location":{"id":"doi:10.1109/tpwrs.2026.3741483","doi":"https://doi.org/10.1109/tpwrs.2026.3741483","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpwrs.2026.3741483","pdf_url":null,"source":{"id":"https://openalex.org/S201921491","display_name":"IEEE Transactions on Power Systems","issn_l":"0885-8950","issn":["0885-8950","1558-0679"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"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 Power Systems","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2503.24152","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057656679","display_name":"Kehao Zhuang","orcid":"https://orcid.org/0000-0001-9813-2308","observed_orcids":["https://orcid.org/0000-0001-9813-2308"]},"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":"Kehao Zhuang","raw_affiliation_strings":["ETH Z\u00fcrich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Z\u00fcrich","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086421717","display_name":"Huanhai Xin","orcid":"https://orcid.org/0000-0001-5327-1371","observed_orcids":["https://orcid.org/0000-0001-5327-1371"]},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huanhai Xin","raw_affiliation_strings":["Zhejiang University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088557739","display_name":"Verena H\u00e4berle","orcid":"https://orcid.org/0000-0002-2735-5237","observed_orcids":["https://orcid.org/0000-0002-2735-5237"]},"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":"Verena H\u00e4berle","raw_affiliation_strings":["ETH Z\u00fcrich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Z\u00fcrich","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157922421","display_name":"Liangxiao Luo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liangxiao Luo","raw_affiliation_strings":["Zhejiang University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153433345","display_name":"Xiaoying Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoying Liu","raw_affiliation_strings":["Zhejiang University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014618966","display_name":"Xiuqiang He","orcid":"https://orcid.org/0000-0002-3755-7553","observed_orcids":["https://orcid.org/0000-0002-3755-7553"]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiuqiang He","raw_affiliation_strings":["Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019393760","display_name":"Linbin Huang","orcid":"https://orcid.org/0000-0002-5892-0374","observed_orcids":["https://orcid.org/0000-0002-5892-0374"]},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Linbin Huang","raw_affiliation_strings":["Zhejiang University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091434894","display_name":"Florian D\u00f6rfler","orcid":"https://orcid.org/0000-0002-9649-5305","observed_orcids":["https://orcid.org/0000-0002-9649-5305"]},"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":"Florian D\u00f6rfler","raw_affiliation_strings":["ETH Z\u00fcrich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Z\u00fcrich","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":2.1645,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.81283412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":92,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10223","display_name":"Microgrid Control and Optimization","score":0.9394999742507935,"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"}},"topics":[{"id":"https://openalex.org/T10223","display_name":"Microgrid Control and Optimization","score":0.9394999742507935,"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"}},{"id":"https://openalex.org/T10305","display_name":"Power System Optimization and Stability","score":0.04729999974370003,"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/T10740","display_name":"Wind Turbine Control Systems","score":0.0010000000474974513,"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/grid-forming-inverters","display_name":"grid-forming inverters","score":0.9620000123977661},{"id":"https://openalex.org/keywords/small-signal-stability","display_name":"small-signal stability","score":0.7409999966621399},{"id":"https://openalex.org/keywords/system-strength","display_name":"system strength","score":0.6449999809265137},{"id":"https://openalex.org/keywords/grid-strength","display_name":"grid strength","score":0.8149999976158142},{"id":"https://openalex.org/keywords/grid-voltage-fluctuation","display_name":"grid voltage fluctuation","score":0.48100000619888306},{"id":"https://openalex.org/keywords/power-system-stability","display_name":"power system stability","score":0.4269999861717224}],"concepts":[{"id":"https://openalex.org/C174348530","wikidata":"https://www.wikidata.org/wiki/Q188635","display_name":"Bridging (networking)","level":2,"score":0.5839999914169312},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5613999962806702},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5519999861717224},{"id":"https://openalex.org/C2778422915","wikidata":"https://www.wikidata.org/wiki/Q10302051","display_name":"Converters","level":3,"score":0.5221999883651733},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5189999938011169},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.5178999900817871},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4860000014305115},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4772000014781952},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.46970000863075256},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.450300008058548},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.44200000166893005},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3946000039577484},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.37040001153945923},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.3472999930381775},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.3206000030040741},{"id":"https://openalex.org/C2983254600","wikidata":"https://www.wikidata.org/wiki/Q1096907","display_name":"Power grid","level":3,"score":0.31929999589920044},{"id":"https://openalex.org/C100776233","wikidata":"https://www.wikidata.org/wiki/Q2532492","display_name":"Bridge (graph theory)","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.2985000014305115},{"id":"https://openalex.org/C2780898871","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Performance metric","level":2,"score":0.2953999936580658},{"id":"https://openalex.org/C37649242","wikidata":"https://www.wikidata.org/wiki/Q932268","display_name":"System of measurement","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C178911571","wikidata":"https://www.wikidata.org/wiki/Q593143","display_name":"Power electronics","level":3,"score":0.2800999879837036},{"id":"https://openalex.org/C108755667","wikidata":"https://www.wikidata.org/wiki/Q1930258","display_name":"AC power","level":3,"score":0.2750999927520752},{"id":"https://openalex.org/C2986219828","wikidata":"https://www.wikidata.org/wiki/Q1193095","display_name":"Coupling strength","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C128624480","wikidata":"https://www.wikidata.org/wiki/Q1504817","display_name":"Low voltage","level":3,"score":0.25440001487731934},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.2531999945640564},{"id":"https://openalex.org/C3019813237","wikidata":"https://www.wikidata.org/wiki/Q65089264","display_name":"Model validation","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tpwrs.2026.3741483","doi":"https://doi.org/10.1109/tpwrs.2026.3741483","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpwrs.2026.3741483","pdf_url":null,"source":{"id":"https://openalex.org/S201921491","display_name":"IEEE Transactions on Power Systems","issn_l":"0885-8950","issn":["0885-8950","1558-0679"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"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 Power Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2503.24152","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2503.24152","pdf_url":"https://arxiv.org/pdf/2503.24152","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:arXiv.org:2510.26953","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2510.26953","pdf_url":"https://arxiv.org/pdf/2510.26953","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2503.24152","doi":"https://doi.org/10.48550/arxiv.2503.24152","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2503.24152","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.48550/arxiv.2510.26953","doi":"https://doi.org/10.48550/arxiv.2510.26953","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.26953","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2503.24152","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2503.24152","pdf_url":"https://arxiv.org/pdf/2503.24152","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":1.0},{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.9090999960899353}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415913622.pdf","grobid_xml":"https://content.openalex.org/works/W4415913622.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4416136997","https://openalex.org/W4416177967","https://openalex.org/W7165340610","https://openalex.org/W4395470948","https://openalex.org/W7077450926","https://openalex.org/W4416136866","https://openalex.org/W7221010523","https://openalex.org/W4411726728","https://openalex.org/W4415745166","https://openalex.org/W4403127394"],"abstract_inverted_index":{"Grid-forming":[0],"(GFM)":[1],"technology":[2],"is":[3,43,127],"widely":[4],"regarded":[5],"as":[6],"a":[7,19,48,61,71,80,96,114,187],"promising":[8],"solution":[9],"for":[10,29,98,190],"future":[11],"power":[12,16,143],"systems":[13],"dominated":[14],"by":[15,103,174],"electronics.":[17],"However,":[18],"universally":[20],"accepted":[21],"definition":[22],"of":[23,37,118,137],"GFM":[24,38,101,178,191],"behavior":[25],"and":[26,53,133,149,156,169,196],"precise":[27],"method":[28],"its":[30,105],"quantification":[31],"remain":[32],"elusive.":[33],"Moreover,":[34],"the":[35,65,68,74,93,99,111,123,131,164,167],"impact":[36],"converter":[39,192],"on":[40],"system":[41,54,112,119,170,181,197],"stability":[42,198],"not":[44],"precisely":[45],"quantified,":[46],"creating":[47],"significant":[49],"disconnect":[50],"between":[51],"device":[52,66,168],"levels.":[55],"To":[56],"address":[57],"these":[58],"gaps":[59],"from":[60],"small-signal":[62],"perspective,":[63],"at":[64],"level,":[67,113],"paper":[69,146],"introduces":[70],"novel":[72],"metric,":[73],"Forming":[75],"Index":[76],"(FI)":[77],"to":[78,83,107,140,153,159],"quantify":[79],"converter's":[81,100],"response":[82],"grid":[84,108,154],"voltage":[85,125,132],"fluctuations.":[86],"Rather":[87],"than":[88],"enumerating":[89],"various":[90],"control":[91],"architectures,":[92],"FI":[94],"provides":[95,186],"metric":[97],"ability":[102],"quantifying":[104],"sensitivity":[106],"variations.":[109],"At":[110],"new":[115],"quantitative":[116],"measure":[117],"strength":[120,155,158],"that":[121,177],"captures":[122],"multi-bus":[124],"stiffness":[126],"proposed,":[128],"which":[129],"quantifies":[130],"phase":[134],"angle":[135],"responses":[136],"multiple":[138],"buses":[139],"current":[141],"or":[142],"disturbances.":[144],"The":[145,183],"further":[147],"extends":[148],"defines":[150],"this":[151],"concept":[152],"bus":[157],"identify":[160],"weak":[161],"areas":[162],"within":[163],"system.":[165],"Finally,":[166],"levels":[171],"are":[172],"bridged":[173],"formally":[175],"proving":[176],"converters":[179],"enhance":[180],"strength.":[182],"proposed":[184],"framework":[185],"unified":[188],"benchmark":[189],"design,":[193],"optimal":[194],"placement,":[195],"assessment.":[199]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2025-11-05T00:00:00"}
