ELK322E POWER TRANSMISSION SYSTEMS
Homework Faulted PTS
Submission Date: June 03, 2022
Name and Family Name:
Q1
Q2
Q3
Student Number:
Total
Q4
Signature:
Students may work together, but cannot write together.
Ö Usta & R Çağlar
PROBLEM 1.
Assume that the unbalanced rms phase voltage and rms current phasors are given
as below.
𝑉𝑎𝑏𝑐
𝑉𝑎
120∠0°
= [𝑉𝑏 ] = [120∠ − 30°] 𝑉,
𝑉𝑐
120∠60°
𝐼𝑎𝑏𝑐
𝐼𝑎
6∠ − 60°
= [𝐼𝑏 ] = [ 6∠30°] 𝐴
𝐼𝑐
6∠180°
(a) Find the three-phase complex power, active and reactive power, apparent
power, and the angle of complex power using phase quantities.
[15pts]
(b) Find the sequence voltages (𝑉012 ) using symmetrical transformation. [20pts]
(c) If the sequence currents (𝐼012 ) are given as below, find the three-phase
complex power using sequence voltages (𝑉012 ) and currents (𝐼012 ). [15pts]
𝐼0
1.0352∠ − 45°
[𝐼1 ] = [
1.0353∠75°] A
𝐼2
5.8185∠ − 69.895°
ELK322E POWER TRANSMISSION SYSTEMS
Homework Faulted PTS
Submission Date: June 03, 2022
PROBLEM 2. A single-line diagram of the power system shown in the Figure, where
negative- and zero-sequence reactances are also given. The neutrals of the generator and
Δ–Y transformers are solidly grounded. The motor neutral is grounded through a
reactance Xn = 0.05 per unit on the motor base.
(a) Draw the per-unit zero-, positive-, and negative sequence networks on a 100-MVA,
13.8-kV base in the zone of the generator.
[15pts]
(b) Reduce the sequence networks to their Thévenin equivalents, as viewed from bus 2.
Pre-fault voltage is VF = 1.05∟0o per unit. Pre-fault load current and Δ –Y
transformer phase shift are neglected.
[10pts]
(c) Calculate the per-unit subtransient fault currents in phases a, b, and c for a bolted
three-phase-to-ground short circuit at bus 2.
[10pts]
(d) Calculate the subtransient fault current in per-unit and in kA for a bolted single lineto-ground short circuit from phase a to ground at bus 2. Also calculate the per-unit
line-to-ground voltages at faulted bus 2.
[15pts]
(e) Calculate the subtransient fault current in per-unit and in kA for a bolted line-to-line
fault from phase b to c at bus 2.
[10pts]