PROBLEMS 619chronous reactance of 2per phase and neg-
ligible armature resistance.
(a) If the motor takes a line current of 350 A op-
erating at 0.8 power factor leading, calculate
the excitation voltage and the power angle.
(b) If the motor is operating on load with a power
angle of−20°, and the excitation is adjusted
so that the excitation voltage is equal in mag-
nitude to the terminal voltage, determine the
armature current and the power factor of the
motor.
13.3.10A 2300-V, three-phase, wye-connected, round-
rotor synchronous motor has a synchronous reac-
tance of 3per phase and an armature resistance
of 0.25per phase. The motor operates on load
with a power angle of−15°, and the excitation is
adjusted so that the internally induced voltage
is equal in magnitude to the terminal voltage.
Determine:
(a) The armature current.
(b) The power factor of the motor.
Neglect the effect of armature resistance.
13.3.11An induction motor takes 350 kW at 0.8 power
factor lagging while driving a load. When an
overexcited synchronous motor taking 150 kW
is connected in parallel with the induction mo-
tor, the overall power factor is improved to 0.95
lagging. Determine the kVA rating of the syn-
chronous motor.*13.3.12An industrial plant consumes 500 kW at a lagging
power factor of 0.6.
(a) Find the required kVA rating of a syn-
chronous capacitor to improve the power
factor to 0.9.
(b) If a 500-hp, 90% efficient synchronous mo-
tor, operating at full load and 0.8 leading
power factor, is added instead of the capaci-
tor in part (a), calculate the resulting power
factor.
13.3.13A three-phase, wye-connected, cylindrical-rotor,
synchronous motor, with negligible armature re-
sistance and a synchronous reactance of 1.27
per phase, is connected in parallel with a three-
phase, wye-connected load taking 50 A at 0.707
lagging power factor from a three-phase, 220-V,
60-Hz source. If the power developed by the mo-
tor is 33 kW at a power angle of 30°, determine:
(a) The overall power factor of the motor and
the load.
(b) The reactive power of the motor.
13.3.14Two identical three-phase, 33-kV, wye-
connected, synchronous generators operating in
parallel share equally a total load of 12 MW
at 0.8 lagging power factor. The synchronous
reactance of each machine is 8per phase, and
the armature resistance is negligible.
(a) If one of the machines has its field excita-
tion adjusted such that it delivers 125 A lag-
ging current, determine the armature current,
power factor, excitation voltage, and power
angle of each machine.
(b) If the power factor of one of the machines is
0.9 lagging, find the power factor and current
of the other machine.
13.3.15A three-phase, wye-connected, round-rotor, 220-
V, 60-Hz, synchronous motor, having a syn-
chronous reactance of 1.27per phase and
negligible armature resistance, is connected in
parallel with a three-phase, wye-connected load
that takes a current of 50 A at 0.707 lagging
power factor and 220 V line-to-line. At a power
angle of 30°, the power developed by the motor is
33 kW. Determine the reactive kVA of the motor,
and the overall power factor of the motor and the
load.
13.3.16A three-phase, wye-connected, 2500-kVA, 6600-
V, 60-Hz turboalternator has a per-phase syn-
chronous reactance and an armature resistance
of 10.4 and 0.071, respectively. Compute the
power factor for zero voltage regulation on full
load.
13.4.1A 100-kW, 250-V shunt generator has an
armature-circuit resistance of 0.05and a field-
circuit resistance of 60. With the generator
operating at rated voltage, determine the induced
voltage at (a) full load, and (b) one-half full load.
Neglect brush-contact drop.
13.4.2A 100-kW, 230-V shunt generator hasRa =
0. 05 andRf= 57. 5 . If the generator oper-
ates at rated voltage, calculate the induced volt-
age at (a) full load, and (b) one-half full load.
Neglect brush-contact drop.
*13.4.3A 10-hp, 250-V shunt motor has an armature-
circuit resistance of 0.5and a field resistance
of 200. At no load, rated voltage, and 1200
r/min, the armature current is 3 A. At full load
and rated voltage, the line current is 40 A, and the
flux is 5% less than its no-load value because of
armature reaction. Compute the full-load speed.