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We assume the distribution network is a line with charging stations located on it. We consider the<jats:italic>Distflow<\/jats:italic>and the<jats:italic>Linearized Distflow<\/jats:italic>models, and we assume that EVs have an exponential charging requirement, that voltage drops on the distribution network stay under control, and that the number of charging stations<jats:italic>N<\/jats:italic>goes to infinity. We investigate the stability of utility-optimizing power allocations in large distribution networks for both power flow models by controlling the arrival rate of EVs to charging stations. For both power flow models, we show that, to obtain stability, the maximum feasible arrival rate, i.e., stability region of vehicles, is decaying as<jats:inline-formula><jats:alternatives><jats:tex-math>$$1\/N^2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mn>1<\/mml:mn><mml:mo>\/<\/mml:mo><mml:msup><mml:mi>N<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, and the difference between those arrival rates is up to constants, which we compare explicitly.<\/jats:p>","DOI":"10.1007\/s11134-023-09873-z","type":"journal-article","created":{"date-parts":[[2023,3,15]],"date-time":"2023-03-15T13:03:14Z","timestamp":1678885394000},"page":"187-239","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Comparison of stability regions for a line distribution network with stochastic load demands"],"prefix":"10.1007","volume":"103","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9611-500X","authenticated-orcid":false,"given":"M. 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