PROBLEMS 615and the core-loss impedance is 400. Using the
T-equivalent circuit of Figure 13.2.5(a):
(a) Calculate the input current and power (i) on
the no-load test (S∼=0) at rated voltage, and
(ii) on a blocked-rotor test (S=1) at rated
voltage.
(b) Corresponding to a slip of 0.05, compute
the input current, torque, output power, and
efficiency.
(c) Determine the starting torque and current;
the maximum torque and the corresponding
slip; and the maximum output power and the
corresponding slip.
For the following parts, use the approximate
equivalent circuit obtained by transferring the
shunt core loss/magnetizing branch to the input
terminals.
(d) Find the same values requested in part (b).
(e) When the machine is driven as an induction
generator with a slip of− 0 .05, calculate the
primary current, torque, mechanical power
input, and electric power output.
(f) Compute the primary current and the braking
torque at the instant of plugging (i.e., reversal
of the phase sequence) if the slip immedi-
ately before plugging is 0.05.13.2.9A 500-hp, wye-connected, wound-rotor induc-
tion motor, when operated at rated voltage and
frequency, develops its rated full-load output at
a slip of 0.02; maximum torque of 2 times the
full-load torque at a slip of 0.06, with a referred
rotor current of 3 times that at full load; and 1.2
times the full-load torque at a slip of 0.2, with a
referred rotor current of 4 times that at full load.
Neglect rotational and stray-load losses. If the
rotor-circuit resistance in all phases is increased
to 5 times the original resistance, determine the
following:
(a) The slip at which the motor will develop the
same full-load torque.
(b) The total rotor-circuit copper loss at full-load
torque.
(c) The horsepower output at full-load torque.
(d) The slip at maximum torque.
(e) The rotor current at maximum torque.
(f) The starting torque.
(g) The rotor current at starting.
13.2.10The per-phase equivalent circuit shown in Fig-
ure 13.2.6 of a three-phase, 600-V, 60-Hz, four-
pole, wye-connected, wound-rotor induction mo-
tor has the following parameters:R 1 = 0. 75 ,
R 2 ′= 0. 80 ,Xl 1 =X′l 2 = 2. 0 , andXm=
50 . Neglect the core losses.
(a) Find the slip at which the maximum devel-
oped torque occurs.
(b) Calculate the value of the maximum torque
developed.
(c) What is the range of speed for stable opera-
tion of the motor?
(d) Determine the starting torque.
(e) Compute the per-phase referred value of the
additional resistance that must be inserted
in the rotor circuit in order to obtain the
maximum torque at starting.
13.2.11A three-phase, wye-connected, 220-V, 10-hp, 60-
Hz, six-pole induction motor (using Figure 13.2.6
for notation) has the following parameters in
ohms per phase referred to the stator:R 1 =
0 .294,R 2 ′= 0 .144,Xl 1 = 0 .503,X′ 12 = 0 .209,
andXm= 13 .25. The total friction, windage,
and core losses can be assumed to be constant at
403 W, independent of load. For a slip of 2.00%,
compute the speed, output torque and power, sta-
tor current, power factor, and efficiency when the
motor is operated at rated voltage and frequency.
Neglect the impedance of the source.
*13.2.12A squirrel-cage induction motor operates at a slip
of 0.05 at full load. The rotor current at starting is
five times the rotor current at full load. Neglecting
stator resistance and rotational and stray-load
losses, and assuming constant rotor resistance,
calculate the starting torque and the maximum
torque in per-unit of full-load torque, as well as
the slip at which the maximum torque occurs.
13.2.13Using the approximate equivalent circuit in
which the shunt branch is moved to the stator in-
put terminals, show that the rotor current, torque,
and electromagnetic power of a polyphase induc-
tion motor vary almost directly as the slip, for
small values of slip.
13.2.14A three-phase, 50-hp, 440-V, 60-Hz, four-pole,
wound-rotor induction motor operates at a slip of
0.03 at full load, with its slip rings short-circuited.
The motor is capable of developing a maximum
torque of two times the full-load torque at rated
voltage and frequency. The rotor resistance per