{"id":"https://openalex.org/W2528940215","doi":"https://doi.org/10.1109/cca.2016.7587824","title":"Solving stochastic AC power flow via polynomial chaos expansion","display_name":"Solving stochastic AC power flow via polynomial chaos expansion","publication_year":2016,"publication_date":"2016-09-01","ids":{"openalex":"https://openalex.org/W2528940215","doi":"https://doi.org/10.1109/cca.2016.7587824","mag":"2528940215"},"language":"en","primary_location":{"id":"doi:10.1109/cca.2016.7587824","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cca.2016.7587824","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Conference on Control Applications (CCA)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/223680","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059695632","display_name":"Tillmann M\u00fchlpfordt","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Tillmann Muhlpfordt","raw_affiliation_strings":["Institute for Applied Computer Science, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Applied Computer Science, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054359566","display_name":"Timm Faulwasser","orcid":"https://orcid.org/0000-0002-6892-7406"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Timm Faulwasser","raw_affiliation_strings":["Laboratoire d'Automatique, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Automatique, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014228448","display_name":"Veit Hagenmeyer","orcid":"https://orcid.org/0000-0002-3572-9083"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Veit Hagenmeyer","raw_affiliation_strings":["Institute for Applied Computer Science, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Applied Computer Science, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5059695632"],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":null,"apc_paid":null,"fwci":5.5639,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.96438889,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"70","last_page":"76"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10305","display_name":"Power System Optimization and Stability","score":0.9932000041007996,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9765999913215637,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/polynomial-chaos","display_name":"Polynomial chaos","score":0.8929938077926636},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.6192394495010376},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6068670749664307},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.6062799096107483},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.596041202545166},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5385227203369141},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5234143733978271},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5230941772460938},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4525732696056366},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.45028433203697205},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4335263669490814},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.241260826587677},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2385188639163971},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23689809441566467},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09364122152328491},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08361813426017761}],"concepts":[{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.8929938077926636},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.6192394495010376},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6068670749664307},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.6062799096107483},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.596041202545166},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5385227203369141},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5234143733978271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5230941772460938},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4525732696056366},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.45028433203697205},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4335263669490814},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.241260826587677},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2385188639163971},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23689809441566467},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09364122152328491},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08361813426017761},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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":3,"locations":[{"id":"doi:10.1109/cca.2016.7587824","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cca.2016.7587824","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Conference on Control Applications (CCA)","raw_type":"proceedings-article"},{"id":"pmh:oai:infoscience.tind.io:223680","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/223680","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"conference proceedings"},{"id":"pmh:oai:tore.tuhh.de:11420/46211","is_oa":false,"landing_page_url":"https://hdl.handle.net/11420/46211","pdf_url":null,"source":{"id":"https://openalex.org/S4306401751","display_name":"tub.dok (Hamburg University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I884043246","host_organization_name":"Hamburg University of Technology","host_organization_lineage":["https://openalex.org/I884043246"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference Paper"}],"best_oa_location":{"id":"pmh:oai:infoscience.tind.io:223680","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/223680","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"conference proceedings"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W605663379","https://openalex.org/W1534416612","https://openalex.org/W1763243278","https://openalex.org/W1967842749","https://openalex.org/W2020934227","https://openalex.org/W2031226561","https://openalex.org/W2036178646","https://openalex.org/W2053792421","https://openalex.org/W2060016034","https://openalex.org/W2066405087","https://openalex.org/W2069722134","https://openalex.org/W2081675961","https://openalex.org/W2105102609","https://openalex.org/W2109894988","https://openalex.org/W2115736354","https://openalex.org/W2120706173","https://openalex.org/W2126082093","https://openalex.org/W2134917918","https://openalex.org/W2135451711","https://openalex.org/W2142657019","https://openalex.org/W2145455389","https://openalex.org/W2156324709","https://openalex.org/W2170540951","https://openalex.org/W2216167945","https://openalex.org/W2292784196","https://openalex.org/W3217167116","https://openalex.org/W4300600608"],"related_works":["https://openalex.org/W2797263970","https://openalex.org/W2891782306","https://openalex.org/W2287391662","https://openalex.org/W339217817","https://openalex.org/W4381886630","https://openalex.org/W2971126152","https://openalex.org/W2103244625","https://openalex.org/W1989122168","https://openalex.org/W2935336655","https://openalex.org/W3152905387"],"abstract_inverted_index":{"The":[0,67],"present":[1],"contribution":[2],"demonstrates":[3],"the":[4,20,41,59,75,86,93],"applicability":[5],"of":[6,22,40,58,100],"polynomial":[7,29,101],"chaos":[8,30],"expansion":[9,31],"to":[10,83,92],"stochastic":[11,42],"(optimal)":[12],"AC":[13],"power":[14,23,27,43],"flow":[15,44],"problems":[16],"that":[17,46,85,104],"arise":[18],"in":[19,50],"operation":[21],"grids.":[24],"For":[25],"rectangular":[26],"flow,":[28],"together":[32],"with":[33],"Galerkin":[34],"projection":[35],"yields":[36,89],"a":[37,51],"deterministic":[38],"reformulation":[39],"problem":[45],"is":[47,106],"solved":[48],"numerically":[49],"single":[52],"run.":[53],"From":[54],"its":[55],"solution,":[56],"approximations":[57,91],"true":[60],"posterior":[61],"probability":[62,94],"density":[63,95],"functions":[64,96],"are":[65],"obtained.":[66],"presented":[68],"approach":[69,88],"does":[70],"not":[71],"require":[72],"linearization.":[73],"Furthermore,":[74],"IEEE":[76],"14":[77],"bus":[78],"serves":[79],"as":[80],"an":[81],"example":[82],"demonstrate":[84],"proposed":[87],"accurate":[90],"for":[97],"low":[98],"orders":[99],"bases,":[102],"and":[103],"it":[105],"computationally":[107],"more":[108],"efficient":[109],"than":[110],"Monte":[111],"Carlo":[112],"sampling.":[113]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}