Method and charging system for charging an electrical energy storage device of an electrically driven vehicle

A method for charging an energy storage device of a vehicle. A charging process of the energy storage device is carried out with a charging device of the vehicle. In a first phase of the charging process, the energy storage device is charged with a first DC voltage of the charging source in dependence on a charging current of the charging source. A battery voltage of the energy storage device is determined during the charging process and is compared with the charging voltage of the charging source. A voltage transformer is operated in dependence on the comparison. In a second phase of the charging process, the energy storage device is charged with a second DC voltage of the voltage transformer in dependence on a choke current of the voltage transformer.