The synchronizing power for one mechanical degree of displacement for a 3-phase, 20000 kVA, 6600 V, 50 Hz, 12-pole machine having X_s = 1.65 Ω and negligible resistance is

Synchronizing power of a synchronous machine is given by,

\({P_{syn}} = 3\frac{{{E_f}{V_t}}}{{{X_s}}}\sin \delta \)

Where E_f is the internally generated emf

V_t is the terminal voltage

X_S is the synchronous reactance

δ is the torque angle

Calculation:

Given that,

\({E_f} = {V_t} = \frac{{6600}}{{\sqrt 3 }}V\)

X_S = 1.65 Ω

Mechanical angle (θ_m) = 1°

Number of poles (P) = 12

Electrical angle, \({\theta _e} = \frac{{{\theta _m}}}{2} \times P = \frac{1}{2} \times 12 = 6^\circ = \frac{\pi }{{30}}rad\)

\(P = 3 \times \frac{{\frac{{6600}}{{\sqrt 3 }} \times \frac{{6600}}{{\sqrt 3 }}\; \times \;\cos 0^\circ }}{{1.65}}\; \times \;\frac{\pi }{{30}}\) 

= 2764.6 kW

= 921.53 kW per phase