PROBLEMS 617(b) If a wye–delta starting method is employed,
find the starting current and the starting
torque.*13.2.22A three-phase, four-pole, 220-V, 60-Hz induction
machine with a per-phase resistance of 0.5is
operating at rated voltage as a generator at a slip
of− 0 .04, delivering 12 A of line current and a
total output of 4000 W. The constant losses from
a no-load run as a motor are given to be 220 W,
of which 70 W represents friction and windage
losses. Calculate the efficiency of the induction
generator.
13.2.23A 2200-V, 1000-hp, three-phase, 60-Hz, 16-pole,
wye-connected, wound-rotor induction motor is
connected to a 2200-V, three-phase, 60-Hz bus
that is supplied by synchronous generators. The
per-phase equivalent circuit of Figure 13.2.6 has
the following parameters:R 1 = 0. 1 =R′ 2 ,
Xl 1 = 0. 625 =X′l 2 , andXm= 20 .Ifthe
machine is driven at a speed of 459 r/min to act as
a generator of real power, find the rotor current
referred to the stator and the real and reactive
power outputs of the induction machine.
13.2.24A three-phase, 440-V, 60-Hz, four-pole induction
motor operates at a slip of 0.025 at full load, with
its rotor circuit short-circuited. This motor is to
be operated on a 50-Hz supply so that the air-gap
flux wave has the same amplitude at the same
torque as on a 60-Hz supply. Determine the 50-
Hz applied voltage and the slip at which the motor
will develop a torque equal to its 60-Hz full-load
value.
13.2.25The rotor of a wound-rotor induction motor is
rewound with twice the number of its original
turns, with a cross-sectional area of the conductor
in each turn of one-half the original value. De-
termine the ratio of the following in the rewound
motor to the corresponding original quantities:
(a) Full-load current.
(b) Actual rotor resistance.
(c) Rotor resistance referred to the stator.
Repeat the problem, given that the original rotor
is rewound with the same number of turns as
originally, but with one-half the original cross-
section of the conductor. Neglect the changes in
the leakage flux.
13.2.26A wound-rotor induction machine, driven by a
dc motor whose speed can be controlled, is op-
erated as a frequency changer. The three-phase
stator winding of the induction machine is ex-
cited from a 60-Hz supply, while the variable-
frequency three-phase power is taken out of the
slip rings. The output frequency range is to be
120 to 420 Hz; the maximum speed is not to
exceed 3000 r/min; and the maximum power
output at 420 Hz is to be 70 kW at 0.8 power
factor. Assuming that the maximum-speed condi-
tion determines the machine size, and neglecting
exciting current, losses, and voltage drops in the
induction machine, calculate:
(a) The minimum number of poles for the induc-
tion machine.
(b) The corresponding minimum and maximum
speeds.
(c) The kVA rating of the induction-machine
stator winding.
(d) The horsepower rating of the dc machine.
13.2.27A^1 / 4 -hp, 110-V, 60-Hz, four-pole, capacitor-
start, single-phase induction motor has the fol-
lowing parameters and losses:R 1 = 2 ,Xl 1 =
2. 8 ,X′l 2 = 2 ,R′ 2 = 4 ,Xm= 70 .
The core loss at 110 V is 25 W, and friction and
windage is 12 W. For a slip of 0.05, compute
the output current, power factor, power output,
speed, torque, and efficiency when the motor is
running at rated voltage and rated frequency with
its starting winding open.
13.2.28The no-load and blocked-rotor tests conducted
on a 110-V, single-phase induction motor yield
the following data:- No-load test: input voltage 110 V, input current 3.7
A, and input power 50 W - Blocked-rotor test: input voltage 50 V and input
current 5.6 A
Taking the stator resistance to be 2.0, friction
and windage loss to be 7 W, and assumingXl 1 =
X′l 2 , determine the parameters of the double-
revolving-field equivalent circuit.
13.2.29The impedance of the main and auxiliary wind-
ings of a^1 / 3 -hp, 120-V, 60-Hz, capacitor-start
motor are given asZ ̄m = 4. 6 +j 3. 8 and
Z ̄a= 9. 6 +j 3. 6 . Determine the value of the
starting capacitance that will cause the main and
auxiliary winding currents to be in quadrature at
starting.
13.3.1A three-phase, wye-connected, cylindrical-rotor
synchronous generator rated at 10 kVA and 230