A separately-excited dc motor is mechanically coupled to a three-phase, four-pole, 30-kVA, 460-V, cylindrical-pole synchronous generator. The dc motor is connected to a constant 230-V dc supply, and the ac generator is connected to a 460-V, fixed-voltage, fixed-frequency, three-phase supply. The synchronous reactance of the synchronous generator is 5.13Ω/phase. The armature resistance of the dc motor is 30 mA. The four-pole dc machine is rated 30 kW at 230 V. All unspecified losses are to be neglected.

a. If the two machines act as a motor-generator set receiving power from the dc source and delivering power to the ac supply, what is the excitation voltage of the ac machine in volts per phase (line-to-neutral) when it delivers 30 kW at unity power factor? What is the internal voltage of the dc motor?

b. Leaving the field current of the ac machine at the value corresponding to the condition of part (a), what adjustment can be made to reduce the power transfer between the two machines to zero? Under this condition of zero power transfer, what is the armature current of the dc machine? What is the armature current of the ac machine?

c. Leaving the field current of the ac machine as in parts (a) and (b), what adjustment can be made to cause the transfer of 30 kW from the ac source to the dc source? Under these conditions what are the armature current and internal voltage of the dc machine? What will be the magnitude and phase of the current of the ac machine?