A rise in the number of EVs (electric vehicles) in Europe is putting pressure on power grids. At an urban scale, Positive Energy Districts (PEDs) are devised as archetypes of (small) urban districts managing a set of interconnected buildings and district elements (lighting system, vehicles, smart grid, etc.). This paper offers a comprehensive analysis of the impact of e-mobility in a PED, simulated using MATLAB-Simulink software. The PED, a small district in northern Spain, is assessed in five scenarios representing varying requirements in terms of energy efficiency of buildings, type of street lighting and number of EVs. The results suggest that the energy rating of the buildings (ranging from A for the most efficient to E) conditions the annual energy balance. A PED with six interconnected buildings (3 residential and 3 of public use) and 405 EVs (as a baseline) only achieves positivity when the buildings have a high energy rating (certificate A or B). In the most efficient case (A-rated buildings), simulation results show that the PED can support 695 EVs; in other words, it can provide nearly 9 million green kilometres. This result represents a potential 71% saving in carbon emissions from e-mobility alone (as compared to the use of fossil-fuel vehicles), thus contributing a reduction in the carbon footprint of the district and the city as a whole.