An electric drive system for driving a machine includes first and second electric drive motors linked to sun and ring gears respectively of a planetary output stage, and a ring brake associated with the ring gear to maintain the ring gear in a locked position. The carrier drives a fixed gear series drive train. In a first regime of operation corresponding to a first range of machine speeds, a controller employs the ring brake to brake the ring gear, and actuates only the first electric drive motor at a speed sufficient to yield the desired machine speed. In a second regime, corresponding to a second range of machine speeds, the controller drives the first electric drive motor at maximum speed, releases the ring brake, and drives the second electric drive motor so as to yield the desired machine speed.