778 BASIC CONTROL SYSTEMS
results. Waveforms caused by the sensors are also shown in Figure 16.1.25. A detailed discussion
of this kind of microprocessor control of current-fed synchronous-motor drives is outside the
scope of this text.(^0180) ° 360 ° ωt
P 1
(^0120) ° 300 ° ωt
P 2
(^060) °
90 °
90 °
Slots
60 ° 60 ° 240 ° ωt
P 3
P 2
P 4
P 3
S′′ S′
P 1
(^0180) °
(b)
(a)
360 ° ωt
P 4
Figure 16.1.25Optical rotor position encoder and its output waveforms.
EXAMPLE 16.1.6
A 1500-hp, 6600-V, six-pole, 60-Hz, three-phase, wye-connected, synchronous motor, with a
synchronous reactance of 36, negligible armature resistance, and unity power factor at rated
power, is controlled from a variable-frequency source with constantV/fratio. Determine the
armature current, torque angle, and power factor at full-load torque, one-half rated speed, and
rated field current. (Neglect friction, windage, and core loss.)
Solution
The simplified per-phase equivalent circuits of the motor are shown in Figure E16.1.6. Phase
voltageV= 6600 /
√
3 = 3810 .6V,and
I ̄m′ =V
0°
jXs
- 6
36 90°
= 105. 9 −90° A
With unity power factor at rated power, we obtain
1500 × 746 =
√
3 × 6600 ×Is
Hence, the rated armature currentIs= 97 .9 A. Then
I ̄f′=I ̄m′−I ̄s′= 105. 9 −90°− 97. 9 0°=− 97. 9 −j 105. 9 = 144. 2 − 132 .8° A
The synchronous speed is( 120 × 60 )/ 6 =1200 rpm, orωs= 125 .7 rad/s. The rated torque is
then
Trated=
1500 × 746 - 7
=8902 N·m