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The uptake of electric vehicles (EVs) may pose a challenge to power distribution networks (PDNs). While smart charging can be deployed to relieve stress on the grid, user-centric smart charging strategies could also exacerbate peak power demand due to synchronization when optimizing charging with regard to different objectives, such as charging costs. In this paper, we assess the charging demand emerging from a large fleet of EVs, with models for the decision to charge and distribution of the steady-state state-of-charge (SoC). These are applied to the municipality of Frederiksberg, Denmark, using data from the Danish national travel survey. Home and workplace charging are mapped to the urban 10 kV medium voltage PDN of Frederiksberg considering different charging behaviors and degrees of synchronization. Results indicate that the likelihood of severe congestion in the power distribution network is low and that it can be attributed to rare scenarios in which high synchronization is observed, particularly when maintaining the normal steady-state demand. Despite the low likelihood, preventive measures should be devised to mitigate such scenarios, especially if additional high-power consumers are connected.