524:
Transients ECE in Power Systems
Session 5; Page 1/2
Spring 2012
ECE 524: Homework #1
Due Session 9 (Feb 1 on campus, February 15 for Engineering Outreach)
Solve each of these problems analytically and then simulate them using a transient
simulation program. Compare your results.
Problem 1. Do the following for the circuit below:
C1 = 60F
R
C2 = 40F
C1
C2
R = 5ohm
The capacitor C1 in the figure has an initial charge of 1.0 Coulomb; C2 is discharged.
Calculate the following:
A. The peak current through the switch
B. The current 200 microseconds after the switch closes
C. The total energy dissipated in the resistor
D. The ultimate energy stored in C2
E. The ultimate voltage on C1
F. Verify that energy is conserved
Problem 2: Given the simple LC network with the conditions given below find the following:
X
C1
C1 = 60F
C2
QC1 = 1C
C2 = 40F
QC2 = 0C
X = 5ohm
A. Find the instantaneous current when the switch closes.
B. Determine the peak current
C. Find the energy stored in the inductor at t = 1ms
D. Find the voltage across C1 at t = 1ms.
at 60Hz
ECE 524:
Transients in Power Systems
Session 5; Page 2/2
Spring 2012
Problem 3. The figure below shows the field coil of an electric machine. It is excited by
closing switch S1 onto an 800V d.c. bus. Determine the energy in stored the coil, and the
energy dissipated in the coil resistance, 1 sec after S1 is closed.
When the coil current has attained a steady value, S1 is opened and S2 is closed
simultaneously. What will be the voltage across S1 0.1 sec later? How much energy will
eventually be dissipated in R2?
S1
Rf
S2
800 V
R2
Lf
Field Coil
+
R2 := 10ohm
Field Coil:
Rf := 3.6ohm
Lf := 2H
Note: when simulation this, S1 needs to be set to interrupt the steady-state
load current
S2 needs to be commanded to close at the same time S1 opens.
Problem 4: A 230kV:69kV, 100MVA three phase transformer (wye grounded-wye grounded)
has per unit leakage reactance of 10% with an X/R ratio of 20. This is supplied by a source
impedance of j0.01pu. No change of base calculations are needed.
A. Calculate the worst case peak fault current for a fault at the low voltage terminals. What
is the angle of inception compared to the voltage waveform (assume a cosine voltage
source)? Include the resistance in this part.
B. Using simulation only, repeat part A if the X/R ratio of the transformer is 7.
Model the system referred to the low voltage winding for your simulation, do not use
the built-in transformer models yet. We will learn to use the transformer models in the
simulation later in the semester.