ECE422:
Power Systems Analysis
Session 9; Page 1/2
Spring 2016
ECE 422: Homework #1
Due Session 12 (February 10)
MVA  MW
pu  1
1. A simple system with the equivalent circuit similar to Figure 7.1 has the parameters given below.
Do the following if a 3 phase fault occurs on phase A:
60 Hz RMS source voltage: VsLL  24kV
Req  0.05ohm
RMS, line-to-line
Leq  2mH
a) Determine the RMS symmetrical fault current
b) Find the switch closing time to create the maximum dc offset in the positive direction.
c) The maximum RMS asymmetrical fault current, assuming the timing of the fault creates
the maximum dc offset.
d) The RMS asymmetrical fault current 3 cycles after the fault occurs (assuming starting
from initiation from for the maximum dc offset)
e) The RMS asymmetrical fault current 3 cycles after the fault occurs, assuming now
that the fault occurs at the point in the voltage wave where the voltage is 300V
(assume the voltage sine wave is rising toward the peak amplitude)
2. The system below has the following parameters:
BUS 1
BUS S
VGen_rated  24kV
24kV
100MVA
24kV: 230kV
100MVA
X = 10%
X/R = 15
-Yg
Line to line
SGen_rated  80MVA
Xd''  0.1pu
Td''  0.05sec
Xd'  0.3pu
Td'  1.0sec
Xd  1.1pu
TA  0.1sec
A fault occurs on the line side of the circuit breaker, and the breaker clears after 3 cycles.
a) Determine the maximum subtransient current (60Hz) through the breaker in pu and amperes (RMS)
b) The RMS asymmetrical current that the breaker interrupts assuming maximum DC offset

Assume the machine is initially unloaded with a 1 pu terminal voltage. Repeat
if the machine is supplying 60MW and 40MVAR (calculate initial prefault
internal voltage).

Neglect the effect of the transformer impedance on the time constants.
ECE422:
Power Systems Analysis
Session 9; Page 2/2
Spring 2016
3. For the system below do the following using per phase circuit analysis:
BUS 1
BUS 2
BUS S
BUS R
RelayR1
13.8kV
100MVA
V = 1.0pu
ZS1 = j0.3 pu
13.8kV: 230kV
100MVA
X = 10%
X/R = 15
-Yg
ZL1 = 0.8 pu
RelayR2
85 o
on 100MVA and 230kV
230:24kV
100MVA
X = 10%
X/R = 15
Yg-
24kV
100MVA
V = 1.0pu
ZR1 = j0.3 pu
A) For a three phase fault 75%of the way from bus 1 to bus 2 (assume Rf=0), determine
(1) the total fault current (magnitude and angle)
(2) the fault current at RelayR1(magnitude and angle)
(3) the voltages at Bus 1 (magnitude and angle)
B) Repeat if the fault resistance is 0.3pu