{"id":"https://openalex.org/W4283694992","doi":"https://doi.org/10.3390/en15134752","title":"Piece-Wise Linear (PWL) Probabilistic Analysis of Power Grid with High Penetration PV Integration","display_name":"Piece-Wise Linear (PWL) Probabilistic Analysis of Power Grid with High Penetration PV Integration","publication_year":2022,"publication_date":"2022-06-28","ids":{"openalex":"https://openalex.org/W4283694992","doi":"https://doi.org/10.3390/en15134752"},"language":"en","primary_location":{"id":"doi:10.3390/en15134752","doi":"https://doi.org/10.3390/en15134752","is_oa":true,"landing_page_url":"https://doi.org/10.3390/en15134752","pdf_url":"https://www.mdpi.com/1996-1073/15/13/4752/pdf?version=1656900236","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://www.mdpi.com/1996-1073/15/13/4752/pdf?version=1656900236","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032756237","display_name":"Giambattista Gruosso","orcid":"https://orcid.org/0000-0001-6417-3750","observed_orcids":["https://orcid.org/0000-0001-6417-3750"]},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giambattista Gruosso","raw_affiliation_strings":["Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci, 32-20133 Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0001-6417-3750","affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci, 32-20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021651870","display_name":"Luca Daniel","orcid":"https://orcid.org/0000-0002-5880-3151","observed_orcids":["https://orcid.org/0000-0002-5880-3151"]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luca Daniel","raw_affiliation_strings":["Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027561141","display_name":"Paolo Maffezzoni","orcid":"https://orcid.org/0000-0001-9778-0039","observed_orcids":["https://orcid.org/0000-0001-9778-0039"]},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Paolo Maffezzoni","raw_affiliation_strings":["Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci, 32-20133 Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0001-9778-0039","affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci, 32-20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027561141"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":{"value":2200,"currency":"CHF","value_usd":2303},"apc_paid":{"value":2200,"currency":"CHF","value_usd":2303},"fwci":0.2041,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.33713244,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":"15","issue":"13","first_page":"4752","last_page":"4752"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.5814999938011169,"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":0.5814999938011169,"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":0.38040000200271606,"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/T10424","display_name":"Electric Power System Optimization","score":0.014499999582767487,"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/probabilistic-analysis","display_name":"probabilistic analysis","score":0.628000020980835},{"id":"https://openalex.org/keywords/distribution-networks","display_name":"distribution networks","score":0.8360000252723694},{"id":"https://openalex.org/keywords/photovoltaic-integration","display_name":"photovoltaic integration","score":0.8379999995231628},{"id":"https://openalex.org/keywords/high-pv-penetration","display_name":"high PV penetration","score":0.9589999914169312},{"id":"https://openalex.org/keywords/gaussian-mixture-model","display_name":"Gaussian mixture model","score":0.9480000138282776},{"id":"https://openalex.org/keywords/power-flow-analysis","display_name":"power flow analysis","score":0.9300000071525574},{"id":"https://openalex.org/keywords/joint-probability-distribution","display_name":"joint probability distribution","score":0.9430000185966492}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.7675656676292419},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.6840758919715881},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.5584186911582947},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.543799877166748},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5201440453529358},{"id":"https://openalex.org/C41291067","wikidata":"https://www.wikidata.org/wiki/Q1897785","display_name":"Photovoltaic system","level":2,"score":0.51307213306427},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.4915851056575775},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.473885715007782},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4689464271068573},{"id":"https://openalex.org/C80107235","wikidata":"https://www.wikidata.org/wiki/Q7162625","display_name":"Penetration (warfare)","level":2,"score":0.42826026678085327},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.4132075309753418},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3005446493625641},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2985081672668457},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.29667139053344727},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1410641372203827},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1325620412826538},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1250591278076172},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.09100934863090515},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0888717770576477},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08207854628562927},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/en15134752","doi":"https://doi.org/10.3390/en15134752","is_oa":true,"landing_page_url":"https://doi.org/10.3390/en15134752","pdf_url":"https://www.mdpi.com/1996-1073/15/13/4752/pdf?version=1656900236","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:dspace.mit.edu:1721.1/143638","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/143638","pdf_url":"https://dspace.mit.edu/bitstream/1721.1/143638/1/energies-15-04752-v2.pdf","source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"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":"Multidisciplinary Digital Publishing Institute","raw_type":"Article"},{"id":"pmh:oai:re.public.polimi.it:11311/1221169","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1221169","pdf_url":"https://re.public.polimi.it/bitstream/11311/1221169/1/energies-15-04752-v2.pdf","source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:RePEc:gam:jeners:v:15:y:2022:i:13:p:4752-:d:850949","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/1996-1073/15/13/4752/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:62cbbb75bf6c4511984078c2c6a3f223","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/62cbbb75bf6c4511984078c2c6a3f223","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 15, Iss 13, p 4752 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/en15134752","doi":"https://doi.org/10.3390/en15134752","is_oa":true,"landing_page_url":"https://doi.org/10.3390/en15134752","pdf_url":"https://www.mdpi.com/1996-1073/15/13/4752/pdf?version=1656900236","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":[{"score":0.9853000044822693,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"},{"score":0.8970999717712402,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283694992.pdf","grobid_xml":"https://content.openalex.org/works/W4283694992.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W2008765185","https://openalex.org/W2018159038","https://openalex.org/W2021258763","https://openalex.org/W2051825270","https://openalex.org/W2083402196","https://openalex.org/W2088511592","https://openalex.org/W2099867508","https://openalex.org/W2131290027","https://openalex.org/W2199800958","https://openalex.org/W2340920670","https://openalex.org/W2568461278","https://openalex.org/W2596479026","https://openalex.org/W2759279362","https://openalex.org/W2793352959","https://openalex.org/W2959720671","https://openalex.org/W2963476176","https://openalex.org/W3000685545","https://openalex.org/W3011030421","https://openalex.org/W3014917440","https://openalex.org/W3022721303","https://openalex.org/W3032442212","https://openalex.org/W3049476145","https://openalex.org/W3086644762","https://openalex.org/W3160303767","https://openalex.org/W3181619191"],"related_works":["https://openalex.org/W4308462601","https://openalex.org/W4415143118","https://openalex.org/W6945292431","https://openalex.org/W4296916878","https://openalex.org/W4221068595","https://openalex.org/W3187297461","https://openalex.org/W4393262298","https://openalex.org/W3112616544","https://openalex.org/W1970095085","https://openalex.org/W7065665505"],"abstract_inverted_index":{"This":[0,114],"paper":[1],"aims":[2],"at":[3],"presenting":[4],"a":[5,26,40,60,102,125],"novel":[6,23],"effective":[7],"approach":[8],"to":[9],"probabilistic":[10,79],"analysis":[11,80],"of":[12,19,34,43,57,63,76,83,92,95,98,118,127],"distribution":[13,91],"power":[14],"grid":[15,109],"with":[16,39,59],"high":[17],"penetration":[18],"PV":[20,36,65,128],"sources.":[21],"The":[22,52],"method":[24,53],"adopts":[25],"Gaussian":[27],"Mixture":[28],"Model":[29],"for":[30],"reproducing":[31],"the":[32,44,55,77,88,93,116,120],"uncertainty":[33,110],"correlated":[35],"sources":[37,66],"along":[38],"piece-wise-linear":[41],"approximation":[42],"voltage-power":[45],"relationship":[46],"established":[47],"by":[48],"load":[49],"flow":[50],"problem.":[51],"allows":[54],"handling":[56],"scenarios":[58],"large":[61],"number":[62],"uncertain":[64],"in":[67,86],"an":[68],"efficient":[69],"yet":[70],"accurate":[71],"way.":[72],"A":[73],"distinctive":[74],"feature":[75],"proposed":[78],"is":[81],"that":[82],"directly":[84],"providing,":[85],"closed-form,":[87],"joint":[89],"probability":[90,117],"set":[94],"observable":[96],"variables":[97],"interest.":[99],"From":[100],"such":[101],"comprehensive":[103],"statistical":[104],"representation,":[105],"remarkable":[106],"information":[107],"about":[108],"can":[111],"be":[112],"deduced.":[113],"includes":[115],"violating":[119],"safe":[121],"operation":[122],"conditions":[123],"as":[124],"function":[126],"penetration.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2022-06-30T00:00:00"}