ECE 4300/5300 ELECTRIC POWER SYSTEMS SPRING 2016 HW #7
DUE: 04/11/2016
NOTE**: There are answers to some of the problems at the end of the book. To get full credit, you must show
how you got your answers or you will receive ZERO score.
1. Consider the radial three-phase network shown in 10 MVA
G1
Fig. P1.1. A solid three-phase fault occurs at F.
15% reactance
Use system base of 100 MVA and the voltage
11 kV
bases are 11 kV in the generators, 33 kV
for the overhead line, and 6.6 kV for the cable.
(a) (i) Determine the per unit values of the
impedances of the network.
(ii) Determine the per unit values of the
voltages of the network.
33 kV
(iii)Draw the equivalent per unit circuit
diagram of the network.
(b) Determine the Thevenin’s equivalent circuit
6.6 kV
at the fault.
(c) Determine the fault current at 11 kV bus under
fault conditions.
(d) Determine the line voltage at the 11 kV bus
under fault conditions.
G2
10 MVA
12.5% reactance
T1
10 MVA
X = 10%
Overhead line: 30 km
z = (0.27 + j0.36) Ω/km
T2
5 MVA
X = 8%
z = (0.135 + j0.08) Ω/km
F
3 km cable
Fig. P1.1
2. The 4-bus power system, shown in Fig. P2.1, buses 1
and 2 are generator buses and 3 and 4 are load buses.
G1
The generators buses are rated 11 kV, 100 MVA,
T1
with transient reactance of 10% each. Both
11/110 kV
transformers are 11/100 kV, 100 MVA with a
1
j0.15
leakage reactance of 5%. The reactances of the
lines to a base of 100 MVA, 110 kV are indicated
j0.2
on the figure. A solid three-phase short-circuit
j0.1
fault occurs at bus 4 (load bus).
j0.15
(a) Draw the equivalent per unit circuit diagram
of the network.
4
(b) Determine the Thevenin’s equivalent circuit
Fault
at the fault.
(c) Determine the fault current at bus 4 under
Fig. P2.1
fault conditions.
(d) Determine the line voltages at the buses 1, 2, 3, and 4 under fault conditions.
(e) Determine the Short-Circuit MVA Capacity.
3
j0.1
2
11/110 kV
T2
G2
3. Consider of Fig. P2.1 of question (2).
(a) Convert the network impedances to admittances.
(b) Determine the bus admittance matrix (Ybus).
(c) Determine the bus impedance matrix (Zbus = [Ybus]-1).
(d) Use the bus impedance matrix to determine the fault current at bus 4 under fault conditions.
(e) Use the bus impedance matrix to determine the line voltages at the buses 1, 2, 3, and 4 under fault
conditions. The prefault voltage condition at the buses: V1(0) = V2(0) = V3(0) = V4(0) = 1.0/0o p.u.
(f) Use the bus impedance matrix to determine the line currents under fault conditions.
4. Power System Analysis by Saadat: Problem #10.5 pp. 492.