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

225 views
in General
closed
The synchronizing power for one mechanical degree of displacement for a 3-phase, 20000 kVA, 6600 V, 50 Hz, 12-pole machine having Xs = 1.65 Ω and negligible resistance is
1. 1024.6 W
2. 921.9 kW
3. 782.6 kW
4. 1182.6 kW

by (48.1k points)
selected

Correct Answer - Option 2 : 921.9 kW

Synchronizing power of a synchronous machine is given by,

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

Where Ef is the internally generated emf

Vt is the terminal voltage

XS is the synchronous reactance

δ is the torque angle

Calculation:

Given that,

${E_f} = {V_t} = \frac{{6600}}{{\sqrt 3 }}V$

XS = 1.65 Ω

Mechanical angle (θm) = 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