In this paper the operation of a double-fed wound-rotor induction machine, coupled to a wind turbine, as a generator at sub-synchronous speeds is investigated. A novel approach is used in the analysis, namely, the rotor power flow approach. The conditions necessary for operating the machine as a double-fed induction generator (DFIG) are deduced. Formulae describing the factors affecting the range of sub-synchronous speeds within which generation occurs are deduced. The variations in the magnitude and phase angle of the voltage injected to the rotor circuit as the speed of the machine changes to achieve generation at the widest possible sub-synchronous speed range is presented. Also, the effect of the rotor parameters on the generation range is presented. The analysis proved that the generation range could increase from sub-synchronous to super-synchronous speeds, which increases the amount of energy captured by the wind energy conversion system (WECS) as result of utilizing the power available in the wind at low wind speeds.