{"id":"https://openalex.org/W3023594465","doi":"https://doi.org/10.3390/e22060666","title":"Power-Law Distributions of Dynamic Cascade Failures in Power-Grid Models","display_name":"Power-Law Distributions of Dynamic Cascade Failures in Power-Grid Models","publication_year":2020,"publication_date":"2020-06-16","ids":{"openalex":"https://openalex.org/W3023594465","doi":"https://doi.org/10.3390/e22060666","mag":"3023594465","pmid":"https://pubmed.ncbi.nlm.nih.gov/33286438"},"language":"en","primary_location":{"id":"doi:10.3390/e22060666","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22060666","pdf_url":"https://www.mdpi.com/1099-4300/22/6/666/pdf?version=1593398034","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/22/6/666/pdf?version=1593398034","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002721807","display_name":"G\u00e9za \u00d3dor","orcid":"https://orcid.org/0000-0001-9259-5352"},"institutions":[{"id":"https://openalex.org/I4210162307","display_name":"HUN-REN Centre for Energy Research","ror":"https://ror.org/05wswj918","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210162307","https://openalex.org/I4387152226"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"G\u00e9za \u00d3dor","raw_affiliation_strings":["Centre for Energy Research, P. O. Box 49, H-1525 Budapest, Hungary"],"raw_orcid":"https://orcid.org/0000-0001-9259-5352","affiliations":[{"raw_affiliation_string":"Centre for Energy Research, P. O. Box 49, H-1525 Budapest, Hungary","institution_ids":["https://openalex.org/I4210162307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039705583","display_name":"B. Hartmann","orcid":"https://orcid.org/0000-0001-5271-2681"},"institutions":[{"id":"https://openalex.org/I4210162307","display_name":"HUN-REN Centre for Energy Research","ror":"https://ror.org/05wswj918","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210162307","https://openalex.org/I4387152226"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"B\u00e1lint Hartmann","raw_affiliation_strings":["Centre for Energy Research, P. O. Box 49, H-1525 Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Energy Research, P. O. Box 49, H-1525 Budapest, Hungary","institution_ids":["https://openalex.org/I4210162307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002721807"],"corresponding_institution_ids":["https://openalex.org/I4210162307"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1690},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1690},"fwci":0.5262,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.68962963,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"22","issue":"6","first_page":"666","last_page":"666"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14444","display_name":"Power Systems and Renewable Energy","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2102","display_name":"Energy Engineering and Power Technology"},"field":{"id":"https://openalex.org/fields/21","display_name":"Energy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T14444","display_name":"Power Systems and Renewable Energy","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2102","display_name":"Energy Engineering and Power Technology"},"field":{"id":"https://openalex.org/fields/21","display_name":"Energy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10305","display_name":"Power System Optimization and Stability","score":0.9940000176429749,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cascade","display_name":"Cascade","score":0.7320364117622375},{"id":"https://openalex.org/keywords/power-grid","display_name":"Power grid","score":0.556804895401001},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.5272765755653381},{"id":"https://openalex.org/keywords/power-law","display_name":"Power law","score":0.4886968433856964},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43261343240737915},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4306575059890747},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3815041780471802},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26217734813690186},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22573614120483398},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.18792253732681274},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10092338919639587}],"concepts":[{"id":"https://openalex.org/C34146451","wikidata":"https://www.wikidata.org/wiki/Q5048094","display_name":"Cascade","level":2,"score":0.7320364117622375},{"id":"https://openalex.org/C2983254600","wikidata":"https://www.wikidata.org/wiki/Q1096907","display_name":"Power grid","level":3,"score":0.556804895401001},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.5272765755653381},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.4886968433856964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43261343240737915},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4306575059890747},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3815041780471802},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26217734813690186},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22573614120483398},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.18792253732681274},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10092338919639587},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e22060666","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22060666","pdf_url":"https://www.mdpi.com/1099-4300/22/6/666/pdf?version=1593398034","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:33286438","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33286438","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":"Journal Article"},{"id":"pmh:oai:real.mtak.hu:109999","is_oa":false,"landing_page_url":"http://real.mtak.hu/109999/1/entropy-22-00666.pdf","pdf_url":"http://real.mtak.hu/109999/1/entropy-22-00666.pdf","source":{"id":"https://openalex.org/S4306400081","display_name":"Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210140733","host_organization_name":"Library and Information Centre of the Hungarian Academy of Sciences","host_organization_lineage":["https://openalex.org/I4210140733"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:2005.03458","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.03458","pdf_url":"https://arxiv.org/pdf/2005.03458","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,"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:pubmedcentral.nih.gov:7517205","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7517205","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:aabe7a1f461e43bf9006cc017a30cefc","is_oa":true,"landing_page_url":"https://doaj.org/article/aabe7a1f461e43bf9006cc017a30cefc","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,"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":"Entropy, Vol 22, Iss 6, p 666 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e22060666","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22060666","pdf_url":"https://www.mdpi.com/1099-4300/22/6/666/pdf?version=1593398034","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8199999928474426,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G140337537","display_name":null,"funder_award_id":"K 109577","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G1787861981","display_name":null,"funder_award_id":"K128989","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G2105779385","display_name":null,"funder_award_id":"K128989","funder_id":"https://openalex.org/F4320336675","funder_display_name":"National Research, Development and Innovation Office"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320326762","display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","ror":null},{"id":"https://openalex.org/F4320328860","display_name":"Magyarorsz\u00e1g Korm\u00e1nya","ror":"https://ror.org/007ekx298"},{"id":"https://openalex.org/F4320336675","display_name":"National Research, Development and Innovation Office","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3023594465.pdf","grobid_xml":"https://content.openalex.org/works/W3023594465.grobid-xml"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W100540007","https://openalex.org/W111157985","https://openalex.org/W261461018","https://openalex.org/W1518465634","https://openalex.org/W1525915547","https://openalex.org/W1738124305","https://openalex.org/W1875112053","https://openalex.org/W1967583305","https://openalex.org/W1986121027","https://openalex.org/W1994801733","https://openalex.org/W1999564681","https://openalex.org/W2002727114","https://openalex.org/W2006064197","https://openalex.org/W2015084265","https://openalex.org/W2016250001","https://openalex.org/W2026734660","https://openalex.org/W2041610233","https://openalex.org/W2049343272","https://openalex.org/W2063372232","https://openalex.org/W2072298344","https://openalex.org/W2075514521","https://openalex.org/W2075724381","https://openalex.org/W2102341323","https://openalex.org/W2103725727","https://openalex.org/W2106253517","https://openalex.org/W2112090702","https://openalex.org/W2112949599","https://openalex.org/W2142238462","https://openalex.org/W2142702648","https://openalex.org/W2168448159","https://openalex.org/W2261357334","https://openalex.org/W2313171746","https://openalex.org/W2410209997","https://openalex.org/W2468886016","https://openalex.org/W2552520915","https://openalex.org/W2786353483","https://openalex.org/W2804302282","https://openalex.org/W2804795558","https://openalex.org/W2900629100","https://openalex.org/W2949328830","https://openalex.org/W2963677627","https://openalex.org/W2964034942","https://openalex.org/W2964098315","https://openalex.org/W2996401213","https://openalex.org/W2996506838","https://openalex.org/W2996661204","https://openalex.org/W3032221237","https://openalex.org/W3049187163","https://openalex.org/W3099975916","https://openalex.org/W3104538690","https://openalex.org/W3125038210","https://openalex.org/W3125369678","https://openalex.org/W3146418138","https://openalex.org/W4234989302","https://openalex.org/W4237078129","https://openalex.org/W4237949704","https://openalex.org/W4244643682","https://openalex.org/W6668507957"],"related_works":["https://openalex.org/W2153719181","https://openalex.org/W1971748923","https://openalex.org/W1566155057","https://openalex.org/W2060986072","https://openalex.org/W2052574922","https://openalex.org/W64588465","https://openalex.org/W3120641340","https://openalex.org/W2117825986","https://openalex.org/W3134067061","https://openalex.org/W2151153743"],"abstract_inverted_index":{"Power-law":[0],"distributed":[1,124,180],"cascade":[2,198],"failures":[3],"are":[4],"well":[5,155],"known":[6],"in":[7,190,236],"power-grid":[8,78],"systems.":[9],"Understanding":[10],"this":[11],"phenomena":[12],"has":[13],"been":[14],"done":[15],"by":[16,218],"various":[17],"DC":[18],"threshold":[19,35],"models,":[20],"self-tuned":[21],"at":[22],"their":[23],"critical":[24],"point.":[25,165],"Here,":[26],"we":[27],"attempt":[28],"to":[29,65,74,178],"describe":[30],"it":[31],"using":[32],"an":[33,232],"AC":[34],"model,":[36],"with":[37,142],"a":[38,75,188],"second-order":[39],"Kuramoto":[40],"type":[41],"equation":[42],"of":[43,45,54,97,113,136,172,231,238],"motion":[44],"the":[46,52,66,81,95,110,127,134,137,143,151,158,162,170,174,191,197,203,213,219,229,239],"power-flow.":[47],"We":[48,100,139,166,186,225],"have":[49,167,211,226],"focused":[50],"on":[51,94,150,157],"exploration":[53],"network":[55],"heterogeneity":[56,132],"effects,":[57],"starting":[58],"from":[59,80,109],"homogeneous":[60],"two-dimensional":[61],"(2D)":[62],"square":[63,116],"lattices":[64],"US":[67,152,204],"power-grid,":[68],"possessing":[69],"identical":[70],"nodes":[71,114],"and":[72,205,210],"links,":[73],"realistic":[76],"electric":[77],"obtained":[79],"Hungarian":[82,159,206,240],"electrical":[83],"database.":[84],"The":[85],"last":[86],"one":[87],"exhibits":[88],"node":[89],"dependent":[90],"parameters,":[91],"topologically":[92],"marginally":[93],"verge":[96],"robust":[98],"networks.":[99],"show":[101],"that":[102],"too":[103,130],"weak":[104],"quenched":[105],"heterogeneity,":[106],"coming":[107],"solely":[108],"probabilistic":[111],"self-frequencies":[112,177],"(2D":[115],"lattice),":[117],"is":[118],"not":[119],"sufficient":[120],"for":[121,202],"finding":[122],"power-law":[123,146],"cascades.":[125],"On":[126],"other":[128],"hand,":[129],"strong":[131],"destroys":[133],"synchronization":[135,163,194],"system.":[138],"found":[140,187],"agreement":[141],"empirically":[144],"observed":[145],"failure":[147],"size":[148,199],"distributions":[149],"grid,":[153],"as":[154,156],"networks":[160],"near":[161],"transition":[164],"also":[168,227],"investigated":[169,228],"consequence":[171],"replacing":[173],"usual":[175],"Gaussian":[176],"exponential":[179],"ones,":[181],"describing":[182],"renewable":[183],"energy":[184],"sources.":[185],"drop":[189],"steady":[192],"state":[193],"averages,":[195],"but":[196],"distribution,":[200],"both":[201],"systems,":[207],"remained":[208],"insensitive":[209],"kept":[212],"universal":[214],"tails,":[215],"being":[216],"characterized":[217],"exponent":[220],"\u03c4":[221],"\u2243":[222],"1.8":[223],".":[224],"effect":[230],"instantaneous":[233],"feedback":[234],"mechanism":[235],"case":[237],"power-grid.":[241]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2020-11-23T00:00:00"}