A wound-rotor induction machine, driven by a dc motor whose speed can be controlled, is operated as a frequency changer. The three-phase stator winding of the induction machine is excited from a 60-Hz supply, while the variable frequency three-phase power is taken out of the slip rings. The output frequency range is to be 120 to 420 Hz; the maximum speed is not to exceed 3000 r/min; and the maximum power output at 420 Hz is to be 70 kW at 0.8 power factor. Assuming that the maximum-speed condition determines the machine size, and neglecting exciting current, losses, and voltage drops in the induction machine, calculate:

(a) The minimum number of poles for the induction machine.

(b) The corresponding minimum and maximum speeds.

(c) The kVA rating of the induction-machine stator winding.

(d) The horsepower rating of the dc machine.