{"id":"https://openalex.org/W7221179975","doi":"https://doi.org/10.3390/fractalfract10110756","title":"Constraint-Embedded Fractal Self-Similar Generation of Synthetic Topologies for Receiving-End Power Grids with Rich Renewable Energy: A Hybrid Metaheuristic Approach","display_name":"Constraint-Embedded Fractal Self-Similar Generation of Synthetic Topologies for Receiving-End Power Grids with Rich Renewable Energy: A Hybrid Metaheuristic Approach","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7221179975","doi":"https://doi.org/10.3390/fractalfract10110756"},"language":"en","primary_location":{"id":"doi:10.3390/fractalfract10110756","doi":"https://doi.org/10.3390/fractalfract10110756","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract10110756","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"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":"Fractal and Fractional","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/fractalfract10110756","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158178475","display_name":"Yue Yu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yue Yu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101847647","display_name":"Yifei Pan","orcid":"https://orcid.org/0009-0005-7076-5943","observed_orcids":["https://orcid.org/0009-0005-7076-5943","https://orcid.org/0009-0008-1153-8515"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yifei Pan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5158028374","display_name":"Changgang Li","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Changgang Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121075612","display_name":"Shuolin Zhang","orcid":"https://orcid.org/0009-0009-8024-6740","observed_orcids":["https://orcid.org/0009-0009-8024-6740"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shuolin Zhang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0009-8024-6740","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5158107294","display_name":"Jingyi Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jingyi Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5158216301","display_name":"Yan Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yan Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5158030711","display_name":"Libo Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Libo Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5158028374","https://openalex.org/A5158178475"],"corresponding_institution_ids":[],"apc_list":{"value":2700,"currency":"CHF","value_usd":3258},"apc_paid":{"value":2700,"currency":"CHF","value_usd":3258},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.6655063,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"11","first_page":"756","last_page":"756"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.7836999893188477,"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":0.7836999893188477,"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":0.12129999697208405,"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":0.030300000682473183,"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/fractal-self-similarity","display_name":"fractal self-similarity","score":0.8069999814033508},{"id":"https://openalex.org/keywords/receiving-end-power-grid","display_name":"receiving-end power grid","score":0.7770000100135803},{"id":"https://openalex.org/keywords/high-renewable-energy-penetration","display_name":"high renewable penetration","score":0.8140000104904175},{"id":"https://openalex.org/keywords/box-counting-dimension","display_name":"box-counting dimension","score":0.8999999761581421},{"id":"https://openalex.org/keywords/correlation-dimension","display_name":"correlation dimension","score":0.6930000185966492},{"id":"https://openalex.org/keywords/short-circuit-level","display_name":"short circuit level","score":0.6790000200271606},{"id":"https://openalex.org/keywords/renewable-energy-curtailment","display_name":"renewable energy curtailment","score":0.6460000276565552},{"id":"https://openalex.org/keywords/load-shedding","display_name":"load shedding","score":0.7490000128746033},{"id":"https://openalex.org/keywords/hybrid-metaheuristic-algorithm","display_name":"hybrid metaheuristic","score":0.652999997138977}],"concepts":[{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.7285000085830688},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6234999895095825},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.5737000107765198},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.542900025844574},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5214999914169312},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.5099999904632568},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49219998717308044},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.4056999981403351},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3962000012397766},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34860000014305115},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3382999897003174},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.31290000677108765},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.31290000677108765},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C188573790","wikidata":"https://www.wikidata.org/wiki/Q12705","display_name":"Renewable energy","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C162494671","wikidata":"https://www.wikidata.org/wiki/Q2845227","display_name":"Fractal analysis","level":4,"score":0.2786000072956085},{"id":"https://openalex.org/C2983254600","wikidata":"https://www.wikidata.org/wiki/Q1096907","display_name":"Power grid","level":3,"score":0.2761000096797943},{"id":"https://openalex.org/C143913944","wikidata":"https://www.wikidata.org/wiki/Q5421952","display_name":"Extension topology","level":4,"score":0.27079999446868896},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.25940001010894775},{"id":"https://openalex.org/C423512","wikidata":"https://www.wikidata.org/wiki/Q383973","display_name":"Electricity generation","level":3,"score":0.25600001215934753},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.2533999979496002}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/fractalfract10110756","doi":"https://doi.org/10.3390/fractalfract10110756","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract10110756","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"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":"Fractal and Fractional","raw_type":"journal-article"},{"id":"doi:10.20944/preprints202610.0514.v1","doi":"https://doi.org/10.20944/preprints202610.0514.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202610.0514.v1","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.3390/fractalfract10110756","doi":"https://doi.org/10.3390/fractalfract10110756","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract10110756","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"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":"Fractal and Fractional","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.9853000044822693,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"},{"score":0.7207000255584717,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1968686485","https://openalex.org/W1969324628","https://openalex.org/W1972716516","https://openalex.org/W1983881467","https://openalex.org/W2013169759","https://openalex.org/W2024456553","https://openalex.org/W2027550434","https://openalex.org/W2056651346","https://openalex.org/W2066077687","https://openalex.org/W2106378689","https://openalex.org/W2107941094","https://openalex.org/W2112090702","https://openalex.org/W2113146118","https://openalex.org/W2126105956","https://openalex.org/W2150593711","https://openalex.org/W2152195021","https://openalex.org/W2165299997","https://openalex.org/W2280435028","https://openalex.org/W2543274172","https://openalex.org/W2594034619","https://openalex.org/W2746656411","https://openalex.org/W2797650755","https://openalex.org/W2799803264","https://openalex.org/W2892727038","https://openalex.org/W2903202375","https://openalex.org/W3148918439","https://openalex.org/W3203400682","https://openalex.org/W7133217227","https://openalex.org/W7133347926","https://openalex.org/W7149939239","https://openalex.org/W7169842987"],"related_works":["https://openalex.org/W2896747358","https://openalex.org/W1511646335","https://openalex.org/W3188259844","https://openalex.org/W4377223917","https://openalex.org/W6908464554","https://openalex.org/W2306056841","https://openalex.org/W2340206942","https://openalex.org/W2609935338","https://openalex.org/W2888907401","https://openalex.org/W2292175390"],"abstract_inverted_index":{"Fractal":[0,46],"geometry":[1],"offers":[2],"a":[3,44,66,95,111,127,156,241],"natural":[4],"language":[5],"for":[6,163],"the":[7,38,57,79,105,115,131,138,164,170,173,187,208,229,233,255,263,270],"self-similarity":[8],"and":[9,27,90,102,125,193,196,240,251],"scale":[10],"invariance":[11],"of":[12,40,60,137,159,172,203,254],"power":[13],"networks,":[14],"yet":[15],"future":[16],"receiving-end":[17,97],"grids":[18,42],"shaped":[19],"by":[20,56],"high":[21,24],"renewable":[22,194],"penetration,":[23],"load":[25,124,197,272],"density":[26],"large":[28],"HVDC":[29],"infeed":[30],"have":[31],"no":[32,147],"historical":[33],"counterpart.":[34],"This":[35],"paper":[36],"formalises":[37],"synthesis":[39],"such":[41],"as":[43,176],"Constrained":[45],"Iteration":[47],"System":[48],"(CFIS),":[49],"in":[50],"which":[51],"synthetic":[52,174],"topology":[53,225],"is":[54],"generated":[55,106],"scale-progressive":[58],"composition":[59],"three":[61],"fractal":[62,148,179,243],"operators,":[63],"each":[64],"coupling":[65],"spatial":[67],"clustering/topology":[68],"operator":[69],"with":[70,123,169,245],"an":[71,177,252],"engineering":[72,143],"constraint-projection":[73],"operator.":[74],"A":[75],"hybrid":[76],"metaheuristic":[77],"realises":[78],"operators":[80],"through":[81],"dynamic-weighted":[82],"K-means":[83],"(DWK-Means),":[84],"social-learning":[85],"particle":[86],"swarm":[87],"optimisation":[88],"(SL-PSO)":[89],"constraint-embedded":[91],"2-opt":[92],"(CE-2-opt).":[93],"On":[94],"provincial":[96],"grid":[98,175],"at":[99,215,220,269],"162,":[100],"234":[101],"363":[103,221],"GW,":[104],"topologies":[107],"are":[108,184],"scale-invariant":[109],"over":[110],"well-defined":[112],"box-size":[113],"range:":[114],"box-counting":[116],"dimension":[117,133,158,244],"rises":[118],"from":[119,213],"1.675":[120],"to":[121,218],"1.800":[122],"shows":[126,206,258],"clear":[128],"voltage-layered":[129],"hierarchy;":[130],"constrained":[132],"remains":[134],"within":[135,186],"1.5%":[136],"unconstrained":[139],"value,":[140],"showing":[141],"that":[142,207,259],"feasibility":[144],"costs":[145],"almost":[146],"quality.":[149],"The":[150],"500":[151],"kV":[152],"station":[153],"set":[154],"attains":[155,236],"correlation":[157],"1.81":[160],"versus":[161],"1.69":[162],"real":[165],"existing":[166],"grid,":[167],"consistent":[168],"interpretation":[171],"idealised":[178],"upper":[180],"bound.":[181],"Short-circuit":[182],"levels":[183],"brought":[185],"63":[188],"kA":[189],"limit":[190],"after":[191],"correction,":[192],"curtailment":[195],"shedding":[198],"remain":[199],"zero;":[200],"N-1":[201],"screening":[202],"all":[204],"elements":[205],"worst":[209],"post-contingency":[210],"loading":[211],"falls":[212],"324.7%":[214],"162":[216],"GW":[217],"141.1%":[219],"GW.":[222],"Against":[223],"classical":[224],"generators":[226],"built":[227],"on":[228],"same":[230],"node":[231],"set,":[232],"proposed":[234],"backbone":[235],"full":[237],"degree-two":[238],"redundancy":[239,256],"comparable":[242],"about":[246],"24%":[247],"less":[248],"line":[249],"length,":[250],"ablation":[253],"bound":[257],"it,":[260],"rather":[261],"than":[262],"short-circuit":[264],"limit,":[265],"governs":[266],"steady-state":[267],"security":[268],"low":[271],"scale.":[273]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-10-10T00:00:00"}