616 ROTATING MACHINES
phase referred to the stator is 0.1. Neglect
the stator resistance and rotational and stray-load
losses. Find the rotor copper loss at full load and
the speed at maximum torque. Compute the value
of the per-phase rotor resistance (referred to the
stator) that must be added in series to produce a
starting torque equal to the maximum torque.
13.2.15A three-phase, 220-V, 60-Hz, four-pole, wye-
connected induction motor has a per-phase stator
resistance of 0.5. The following no-load and
blocked rotor test data on the motor are given:
- No-load test: line-to-line voltage 220 V, total
input power 600 W, of which 200 W is the
friction and windage loss, and line current 3 A - Blocked-rotor test: line-to-line voltage 35 V,
total input power 720 W, and line current 15 A
(a) Calculate the parameters of the equivalent
circuit shown in Figure 13.2.5(c).
(b) Compute the output power, output torque,
and efficiency if the machine runs as a motor
with a slip of 0.05.
(c) Determine the slip at which maximum torque
is developed, and obtain the value of the
maximum torque.
Note:It may help the student to solve Problems
13.2.15 through 13.2.17 if the background given
in the solutions manual as part of the solution to
Problem 13.2.15 is provided.
13.2.16The synchronous speed of a wound-rotor induc-
tion motor is 900 r/min. Under a blocked-rotor
condition, the input power to the motor is 45 kW
at 193.6 A. The stator resistance per phase is 0.2
, and the ratio of effective stator turns to effec-
tive rotor turns is 2. The stator and rotor are both
wye-connected. Neglect the effect of the core-
loss and magnetizing impedances. Calculate:
(a) The value in ohms of the rotor resistance per
phase.
(b) The motor starting torque.
13.2.17The no-load and blocked-rotor tests on a three-
phase, wye-connected induction motor yield the
following results: - No-load test: line-to-line voltage 400 V, input
power 1770 W, input current 18.5 A, and fric-
tion and windage loss 600 W - Blocked-rotor test: line-to-line voltage 45 V,
input power 2700 W, and input current 63 A
Determine the parameters of the equivalent cir-
cuit of Figure 13.2.5(a), assumingR 1 =R′ 2 and
Xl 1 =X′l 2.
*13.2.18A three-phase induction motor has the per-phase
circuit parameters shown in Figure P13.2.18. At
what slip is the maximum power developed?
13.2.19A large induction motor is usually started by
applying a reduced voltage across the motor; such
a voltage may be obtained from an autotrans-
former. A motor is to be started on 50% of full-
load torque, and the full-voltage starting current
is 5 times the full-load current. The full-load slip
is 4%. Determine the percentage reduction in the
applied voltage (i.e., the percentage tap on the
autotransformer).
13.2.20A three-phase, 400-V, wye-connected induction
motor takes the full-load current at 45 V with the
rotor blocked. The full-load slip is 4%. Calculate
the tappingskon a three-phase autotransformer
to limit the starting current to 4 times the full-
load current. For such a limitation, determine the
ratio of starting torque to full-load torque.
13.2.21A three-phase, 2200-V, 60-Hz, delta-connected,
squirrel-cage induction motor, when started at
full rated voltage, takes a starting current of 693
A from the line and develops a starting torque of
6250 N·m.
(a) Neglect the impedance and the exciting cur-
rent of the compensator. Calculate the ra-
tio of a starting compensator (i.e., an auto-
transformer starter) such that the current sup-
plied by the 2200-V line is 300 A. Compute
the starting torque with the starting compen-
sator.
+−V 1 Xm = 20 ΩR 1 = 0.05 ΩI' 2
Xl 1 + X'l 2 = 0.3 Ω= Ω
R' 2
S0.05
SFigure P13.2.18