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This paper quantifies the impact of single-phase on-board charging strategies for electric vehicles (EVs) in a case study of a heavily loaded unbalanced Flemish three-phase low-voltage residential grid. Voltage droop charging and EV-based peak shaving, which do not need communication with the distribution grid, are modeled and the results are compared. The grid voltages are analyzed according to the probabilistic and deterministic limits of the EN50160 standard, for a 100% EV penetration rate. The impact on the EV user comfort is evaluated in terms of charging time and electrically driven distances. The chosen voltage droop charging eliminates critical voltages below 0.85 pu and reduces voltage unbalance, with a limited impact on the total charging time. EV-based peak shaving makes the grid fully compliant with EN50160 and avoids the need for an infrastructure upgrade. The electrically driven distances are not influenced by the charging strategies.