A 3-phase, 15-kV, 4-pole, cylindrical rotor synchronous generator is connected to a 50-Hz infinite bus. The synchronous reactance of the machine is X_s = 0.6 ohms per phase and the excitation voltage is set to E₀ = 12 kV line-to-neutral. 

 a)  Draw single-phase equivalent circuit representing the machine connected to infinite bus. 

b)  Consider the machine running as a synchronous condenser.

(i)  What is the amount of active power generated by the machine? 

(ii)  Calculate the amount of current injected by the machine to the infinite bus. 

(iii)  Calculate the amount of reactive power generated by the machine. 

 Now, the excitation voltage has been reduced to 8.66 kV and the steam turbine supplies mechanical torque on the shaft such that the torque angle of the machine is equal to +30°.

 c)  Draw phasor diagram for this operating conditions showing clearly the bus voltage, the excitation voltage and the stator current. 

d)  Calculate the machine power factor.