Question:

A 3-phase, 15 kV, 4-pole, cylindrical rotor synchronous generator is connected to infinite bus running at 50 Hz. The synchronous reactance of the machine is X_s = 0.6 Ω per phase and the excitation voltage is set to E₀ = 12 kV line-to-neutral. The mechanical torque applied to the generator is equal to 1591 kNm. 

Considering these operating conditions:

(a)  Calculate the power generated under these conditions.

(b)  Calculate the power angle at which the generator is operating.

(c)  Sketch a phasor diagram showing the excitation voltage, the bus voltage and the stator current of the generator.

(d)  Determine from the phasor diagram whether the power factor is leading or lagging under these conditions.

(e)  Calculate the amount of active and reactive power exchanged between the generator and the infinite bus.