The disclosure relates to a drive system for an electric vehicle, comprising an electric motor, a traction battery for supplying the electric motor, an asynchronous machine, and a combustion engine for driving the asynchronous machine, wherein the asynchronous machine is arrange for charging the traction battery upon a control signal to extend the range of the electric vehicle. The traction battery has a plurality of a battery lines having adjustable output voltage for generating voltage progressions which are phase-shifted relative to one another, and each battery pack line is not only provided for supplying one of the phase connections of the electric motor but is also connected to a phase connection of the asynchronous machine. The disclosure further relates to a corresponding method for charging a traction battery having a plurality of battery lines by means of an asynchronous machine and a combustion engine disposed in series therewith.