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Electric Vehicles (EVs) are considered as one of the important components of the future intelligent grids. Their role as energy storages in the electricity grid could provide local sustainable solutions to support more renewable energy. In order to estimate the extent of interaction of EVs in the electricity grid operation, a careful examination in the local electricity system is essential. This paper investigates the degree of EV penetration and its key influence on the low voltage distribution grids. Three detailed models of residential grids in Denmark are considered as test cases in this study, where alternate and flexible domestic solutions like EVs are inevitable for integrating the increasing amount of variable wind power. The result from these analyses shows that the individual feeder capabilities of handling an increasing amount of EV loads, is varied from 0-40% on an hourly basis. Also it is shown that there is enough head-space on the transformer capacity which can be used to charge many EVs during a day. The overall transformer capability of handling EV loads varies between 6-40% for peak and minimum demand hours, which is dependent on the robustness of the grids. The voltage drops are reflected as the major technical constraint to the stable operation of the electricity grids for integrating more EVs, when compared to the thermal loading on the cables.