tutorial synchronous machine

TUTORIAL
SYNCHRONOUS MACHINE
1. A 25 kVA, 220 V, 3- phase synchronous generator delivers rated kVA at a power factor of 0.8 lagging. The
armature resistance is 0.2 ohm/phase and synchronous reactance is 0.6 ohm/phase. The friction and
windage losses are 460 W and core loss is 610 W. Calculate the voltage regulation and efficiency at fullload.
2. A 3-phase Y-connected synchronous generator is rated at 120 MVA, 13.2 kV, 0.8 power factor lagging
with 60 Hz frequency. Its synchronous reactance is 0.7 Ω and armature resistance is negligible. Calculate
the voltage regulation of this generator.
[34.6 %]
3. A 3-phase synchronous generator operates on to a 13.8 kV power grid. The reactance is 5 ohm/phase. It
is delivering 12 MW and 6 MVar (inductive) to the system. Determine
a. Power angle
b. Phase angle
c. Generated emf
[a. 15.2 ° b. 26.6° c. 16.56 kV]
4. A 480 V 60 Hz 6-pole motor draws 50 A from the line at unity power factor and the full load. Assuming
that the losses are negligible. Calculate
a. The output torque
b. The magnitude of the line of the power factor is adjusted to 0.8 leading.
[a. 331 Nm b. 62.5 A]
5. A 480 V 400 hp 60 Hz 8-pole star-connected synchronous motor has a per phase synchronous reactance
of 1 Ω and negligible armature resistance. If the friction, windage and core loss is negligible, calculate
the magnitude of Ea and Ia at 0.85 power factor lagging. What is the torque produced?
[408 V, 422 A, 3166 Nm]
6. A 2300 V 100 hp 60 Hz 8-pole Y-connected synchronous motor has a rated power factor of 0.85 leading.
At full load, the efficiency is 85 %. The armature resistance is 1.1 Ω and the synchronous reactance is 20
Ω per phase. Find the following quantities at full load
a. Output torque
b. Input power
c. Mechanical power
d. Ea
e. Ia
f. Draw the phasor diagram.
[a. 792 Nm b. 87.8 kW c. 85.6 kW d. 1641 V e. 25.9 A]
7. A 2200 V 500 hp 3-phase Y-connected motor has a resistance of 0.3 Ω and synchronous reactance of 3 Ω
per phase respectively. Determine the inductive emf per phase of the motor on full load with efficiency
of 94 % and power factor of 0.8 leading.
[1510 V]
8. A 400 V 10 hp 3-phase synchronous motor has a negligible armature resistance and synchronous
reactance of 10 ohm/phase. Determine the minimum current and corresponding induced emf for full
load conditions. Assume the efficiency is 85%.
2
9. A 480-V, 60 Hz, six-pole synchronous motor draws 80 A from the line at unity power factor and full load.
Assuming that the motor is lossless, answer the following questions:
a. What is the output torque of this motor?
b. What must be done to change the power factor to 0.8 leading? Explain your answer, using phasor
diagrams.
c. What will the magnitude of the line current be if the power factor is adjusted to 0.8 leading?
[a. 529 Nm c. 100 A]
10. A 480-V, 60 Hz, 400-hp 0.8-PF-leading eight-pole D-connected synchronous motor has a synchronous
reactance of 1.0 Ω and negligible armature resistance. Ignore its friction, windage, and core losses for
the purposes of this problem.
a. If this motor is initially supplying 400 hp at 0.8 PF lagging, what are the magnitudes and angles of
EA and IA ?
b. How much torque is this motor producing? What is the torque angle?
[a. 259 Ð 36.87° A, 385 Ð− 32.6 V b. 3166 N m]