618 ROTATING MACHINES
V has a synchronous reactance of 1.5per phase
and an armature resistance of 0.5per phase.
(a) Determine the voltage regulation at full load
with: (i) 0.8 lagging power factor, and (ii) 0.8
leading power factor.
(b) Calculate the power factor for which the volt-
age regulation becomes zero on full load.
13.3.2A three-phase, wye-connected, 2300-V, four-
pole, 1000-kVA, 60-Hz synchronous machine
has a synchronous reactanceXs= 5 , a field re-
sistanceRf= 10 , and an approximately linear
magnetization characteristic (EfversusIf) with
a slopeKag= 200 . The machine is connected
to a balanced three-phase ac system and is used
as a generator. Determine the following:
(a) The rated stator current.
(b) The exciter settingVex=IfRffor operating
the machine at rated conditions, at a power
factor of (i) 0.866 lagging and (ii) 0.866
leading.
(c)Vexin part (b) for unity power factor and the
same real power output as in part (b).
(d) The complex power delivered by the gener-
ator to the system for parts (b) and (c).
13.3.3The loss data for the synchronous generator of
Problem 13.3.2 are:Open-circuit core
loss at 13.8 kV 70 kW
Short-circuit load
loss at 418 A, 75°C 50 kW
Friction and windage
loss 80 kw
Field-winding resis-
tance at 75°C 0.3
Stray-load loss at
full load 20 kWDetermine the efficiency of the generator at rated
load, rated voltage, and 0.8 power factor lagging.
13.3.4A three-phase, six-pole, wye-connected syn-
chronous generator is rated at 550 V and has
a synchronous reactanceXs= 2 . When the
generator supplies 50 kVA at rated voltage and
a power factor of 0.95 lagging, find the arma-
ture currentIaand the excitation voltageEf.
Sketch the phasor diagram ofV ̄t,I ̄a, andE ̄f.
Also, determine the regulation corresponding to
the operating conditions.
13.3.5The synchronous machine of Problem 13.3.2 is
to be used as a motor. Determine the following:(a) The exciter settingVexfor operation at rated
conditions and a power factor of (i) 0.866
lagging, and (ii) 0.866 leading.
(b)Vexin part (a) for unity power factor and the
same real power input as in part (a).
(c) The complex power absorbed by the ma-
chine in parts (a) and (b).
13.3.6For a 45-kVA, three-phase, wye-connected, 220-
V synchronous machine at rated armature cur-
rent, the short-circuit load loss (total for three
phases) is 1.80 kW at a temperature of 25°C. The
dc resistance of the armature at this temperature
is 0.0335per phase. Compute the effective
armature ac resistance in per unit and in ohms
per phase at 25°C.
*13.3.7A 4000-V, 5000-hp, 60-Hz, 12-pole synchronous
motor, with a synchronous reactance of 4per
phase (based on cylindrical-rotor theory), is ex-
cited to produce unity power factor at rated load.
Neglect all losses.
(a) Find the rated and maximum torques.
(b) What is the armature current corresponding
to the maximum torque?
13.3.8A three-phase, wye-connected, four-pole, 400-
V, 60-Hz, 15-hp synchronous motor has a syn-
chronous reactance of 3per phase and negligi-
ble armature resistance. The data for its no-load
magnetization curve follow:
Field current, A:
2 3.5 4.4 6 8 10 12
Line-to-neutral voltage, V:
100 175 200 232 260 280 295(a) When the motor operates at full load at 0.8
leading power factor, determine the power
angle and the field current. Neglect all losses.
(b) Compute the minimum line current for the
motor operating at full load and the corre-
sponding field current.
(c) When the motor runs with an excitation of 10
A while taking an armature current of 25 A,
calculate the power developed and the power
factor.
(d) If the excitation is adjusted such that the
magnitudes of the excitation voltage and the
terminal voltage are equal, and if the motor
is taking 20 A, find the torque developed.
13.3.9A three-phase, wye-connected, 2300-V, 60-Hz,
round-rotor synchronous motor has a syn-