0195136047.pdf

13.3 SYNCHRONOUS MACHINES 589

Efm=

√

13282 + 941. 52 =1628 V

Pmax=

EfmVt

Xsm

=

1628 × 1328

5

= 432 .4 kW per phase, or 1297.2 kW for three phases

Synchronous speed=

120 × 60

20

=360 r/min, or 6 r/s

ωs= 2 π× 6 = 37 .7 rad/s

Tmax=

1297. 2 × 103

37. 7

=34,408 N·m

(b) With the synchronous generator as the power source, the equivalent circuit and the

corresponding phasor diagram for the given conditions are shown in Figure E13.3.2(b),

with subscriptgattached to the generator quantities,

Efg=Efm=1628 V

Pmax=

EfgEfm

Xsg+Xsm

=

1628 × 1628

10

=265 kW per phase, or 795 kW for three phases

Tmax=

795 × 103

37. 7

=21,088 N·m

If a load torque greater than this amount were applied to the motor shaft, synchronism

would be lost; the motor would stall, the generator would tend to overspeed, and the

circuit would be opened by circuit-breaker action.

Corresponding to the maximum load, the angle betweenE ̄fgandE ̄fmis 90°. From

the phasor diagram it follows that

Vt=

Efg

√

2

=

1628

√

2

= 1151 .3 V line-to-neutral, or 1994 V line-to-line

IagXsg= 1151 .3orIag=

1151. 3

5

=230 A

The power factor is unity at the terminals.

(c)Vt=1328 V, and the angle betweenE ̄fgandE ̄fmis 90°. Hence it follows that

Efg=Efm= 1328

√

2 =1878 V

Pmax=

EfgEfm

Xsg+Xsm

=

1878 × 1878

10

=352.7 kW per phase, or 1058 kW for three phases

Tmax=

1058 × 103

37. 7

=28,064 N·m

Effects of Saliency and Saturation

Because of saliency, the reactance measured at the terminals of a salient-pole synchronous machine
as opposed to a cylindrical-rotor machine (with uniform air gap) varies as a function of the rotor