ECE 3614 HW # 4
1.
A three-phase, eight-pole, 60-Hz synchronous generator has a 50-mWb flux per pole. The stator winding factor is 0.90. The armature has 104 turns per phase. Calculate the induced voltage.

2.
A three-phase, 60-Hz synchronous generator operating at no load has an induced voltage of
4300 V at rated frequency. The pole flux is increased by 10% and the rotor speed is increased by
5%. a.
Calculate the induced voltage. b.
Calculate the frequency.

3.
A three-phase, 100 kVA, 240 V, 60 Hz, six pole, wye connected synchronous generator is supplying a load of 80 kVA at 230 V and 0.866 power factor lagging. The armature has a synchronous impedance of 0.1 + j0.5 Ω per phase. From this information calculate the following: a.
Armature current. b.
Excitation voltage. c.
Power angle. d.
Input shaft torque (no rotational loss).

4.
A cylindrical rotor synchronous generator has a per-unit synchronous reactance of 1.0 and a negligible armature resistance. The generator supplies rated kVA to a load at a terminal voltage of 1.0 per unit and a leading power factor of 80%. Determine the excitation voltage.

5.
The following readings are taken from the results of open-circuit and short-circuit tests on a three phase, 10 MVA, 12 kV, two pole, 60 Hz cylindrical rotor generator driven at synchronous speed.
This generator delivers rated power to a load at 0.8 power factor lagging.
I f
(A) 150 180 200 250 300 350
I
SCC
(A) 400 480
V
OCC
(kV
LL
) 11.2 12.0 12.5 13.5 14.3 14.8
V air-gap
(kV
LL
) 13.5 15.0 a.
Calculate the unsaturated synchronous reactance, both Ω/phase and in per unit. b.
Calculate the saturated synchronous reactance, both Ω/phase and in per unit. c.
Calculate the required field current for the load.
𝐸 𝑎
= 𝑉 𝑡
+ 𝑗𝑋 𝑠
𝐼 𝑎
= 6928.2 + 𝑗(14.43)(481∠ − 36.9°)
= 12,406∠26.6° 𝑉
𝐿𝑁
= 21,488∠26.6° 𝑉
𝐿𝐿
𝐼 𝑓
= (
21,488
12,000
) (180) = 322 𝐴

6.
The generator tested in problem 5 additionally has the provided loss data.
Open-circuit core loss at 12 kV = 75 kW
Short-circuit load loss at 480 A = 60 kW
Friction and windage loss: 65 kW
Field winding resistance: 0.35 Ω a.
For a rated load at 0.8 power factor lagging, calculate voltage regulation and efficiency. b.
For a rated load at unity power factor, calculate voltage regulation and efficiency. c.
For a rated load at 0.8 power factor leading, calculate voltage regulation and efficiency.

7.
A salient-pole synchronous generator has d-axis and q-axis synchronous reactances of 1.6 pu and
1.2 pu, respectively. The generator is connected to an infinite bus through an external reactance of 0.2 pu. The generator delivers is rated output power at 0.8 power factor lagging to the infinite bus. a.
Draw a phasor diagram showing the bus voltage, the armature current, the generator terminal voltage, the excitation voltage, and the rotor angle. b.
Calculate the rotor angle in degrees. c.
Compute the per-unit terminal and excitation voltages.