A 3 ϕ cylindrical-rotor synchronous machine (SM) and a separately excited dc machine (DCM) are mechanically coupled to transfer power from a dc source to an ac source and vice versa. The ratings of the machines are

SM: 12 kVA, 208 V, Xs=3.0 Ω 

DCM: 12 kW, 220 V, RA=0.3 Ω

Considering only the losses in DCM’s armature resistance RA. All other losses are neglected. The DCM is connected to a 220 V dc bus, and the SM is connected to a 3f, 208 V, 60 Hz bus.

1. a) The power is transferred from dc source to the ac source, when the SM is delivering full load at unity power factor,

1) Find the excitation voltage, Ef, and the power angle, d of the SM

2) Find the back-emf,Ec, of the DCM

b) For zero power transfer, while the excitation current of the synchronous machine is left at the value corresponding to the condition of part a)

1) Explain how we can realize zero power transfer between the two machines and determine the armature current in the dc machine

2) Determine the current and power factor of the synchronous machine.

c) Ten-kilowatt is to be transferred from the SM to the DCM.

1. Excitation of the SM is kept the same as in a). What adjustment is necessary to make the transfer from ac to dc possible? Determine the DCM, EG, and its armature current 

2. Determine the power angle of the SM

3. Determine the stator current and power factor of the SM