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This paper's research question is to evaluate the potential impact of large numbers of battery electric vehicles (BEVs) on the future electric grid, and whether the flexibility of BEV charging can induce enough system benefits to remunerate BEV users for the change in their recharging pattern. The considered scenario refers to the Italian situation and what might occur through the year 2040, where a share of BEV stock of 40% can be foreseen, as well as significant increases in PV and wind generation. Although this study is focused on Italy, its results are applicable, with minor differences, to several EU countries. This paper first shows that the future impact of increasing penetration of BEVs appears to be compatible with the expected growth of generation from renewable energy sources (RES) and the corresponding reduction in fossil fuel-based generation. It also gives an estimate of the CO2 emission reduction resulting from these changes, considering an unmanaged BEV charge profile and two different managed profiles that shift the car's charging period to hours of the day when they have no negative impact on the grid and maximize the utilization of RES. Finally, it shows an evaluation of the economic benefits of displacing private car charging ranging from 4 to 10 cEUR/kWh, which could be used as tariff incentives to stimulate this displacing in recharging time. [ABSTRACT FROM AUTHOR]