The growing number of electric vehicles (EV) is challenging the traditional distribution grid with a new set of consumption curves. We employ information from individual meters at charging stations that record the power drawn by an EV at high temporal resolution (i.e., every minute) to analyze and model charging habits. We identify five types of batteries that determine the power an EV draws from the grid and its maximal capacity. In parallel, we identify four main clusters of charging habits. Charging habit models are then used for forecasting at short and long horizons. We start by forecasting day-ahead consumption scenarios for a single EV. By summing scenarios for a fleet of EVs, we obtain probabilistic forecasts of the aggregated load, and observe that our bottom-up approach performs similarly to a machine-learning technique that directly forecasts the aggregated load. Secondly, we assess the expected impact of the additional EVs on the grid by 2030, assuming that future charging habits follow current behavior. Although the overall load logically increases, the shape of the load is marginally modified, showing that the current network seems fairly well-suited to this evolution.