Plug in electric vehicles (PEVs) are expected to play a significant role not only for the economic and environmental benefits they involve but also for the ancillary services they can provide to the supplying grid. However, the inclusion of the electrical vehicles in distribution systems leads to a series of challenges in grid operation. The PEVs battery chargers include static converters that can cause high waveform distortion levels in the line currents and bus voltages of the grid. Then, a harmonic analysis of the whole system is mandatory to avoid the well know detrimental effects of waveform distortions. This paper proposes to apply the Iterative Harmonic Analysis (IHA) to assess the waveform distortion levels of a low voltage distribution system including a high number of PEVs battery chargers. This method guarantees high results accuracy since it considers the interactions between the supply voltage distortion and the battery charger current harmonics; moreover, it allows to know the electrical state of the distribution systems both at the fundamental and at harmonic frequencies. In the last part of the paper, the IHA is applied to assess the harmonic distortions of the Cigré European LV Unbalanced Distribution Network, considering different number and location of single phase and three phase battery chargers.