2004 Exam1 With Solutions
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8/13/2019 2004 Exam1 With Solutions
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EE4721 EXAM 1 October 13, 2004 SOLUTIONS Page 1
PROBLEM 1: (25 points)
In the figure below you are given a balanced three phase network with a generator, a transmission
line, a set of transformers and two balanced three phase loads.
The three phase power drawn by the loads:
LOAD 1 is 100 kVA at 0.95 power factor leading.
LOAD 2 is 100 kVA at 0.95 power factor lagging.
The magnitude of the Line to Line voltage at the loads is 4400 volts.
The transmission line series impedance is 5+j0 ohms in each phase.
Find
A) The line current and the P+jQ for LOAD 1
B) The line current and the P+jQ for LOAD 2
C) The Line to Line voltage magnitude at the generator terminals.
D) The P+jQ supplied by the generator
Transmission line LOAD 1 LOAD 2
a
b
c
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EE4721 EXAM 1 October 13, 2004 SOLUTIONS Page 2
PROBLEM 2: (25 points)
The system below has one generator connected to a high voltage bus through a stepup transformer T1.
The high voltage generator bus is connected to a transmission line. A load is connected through a step
down transformer T2 at the generator bus.
The equipment or nameplate values for the components are:
G1: 1000 MVA, at 22 KV, Xgen=0.6 pu referred to the generator base, G1 is operating at 21 kv
T1: 1200 MVA, 22Kv to 115Kv, Xt1 = 0.15 per unit referred to the low voltage side
T2: 400 MVA, 12Kv to 115Kv, Xt2 = 0.08 per unit referred to the low voltage side
Line: Zline = 4+j6 ohms (actual impedance)
LOAD: 90 MW and 15MVAR lagging
1) Show all the voltage regions on the original network diagram and label them with their base voltage.
2) Draw the complete per unit network, show all per unit impedances using a network (or system) base of
100 MVA
3) Calculate the per unit voltage at G1
4) Calculate the per unit P and Q at the load
GENERATOR
LOAD
LINE
T1
G1
T2
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EE4721 EXAM 1 October 13, 2004 SOLUTIONS Page 3
Problem 3: (20 points)
You are given the per unit parameters for a transmission line shown below:
where Zseries = 0 + j0.8 per unit
and
Ycap = 0 + j0.2 per unit
This problem asssumes that there is no load at bus j, and that is there is no current flow from bus j
(that is, the line is opened at the bus j end).
The voltage at bus j is assumed to be 1.2 per unit volts at zero degrees
Find:
A) The per unit voltage and current at bus i
Ycap/2
i j
Zseries
Ycap/2
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EE4721 EXAM 1 October 13, 2004 SOLUTIONS Page 4
Problem 4: ( 30 points)
For the three bus power system below (line impedances are given in per unit):
Bus 1: GENERATOR BUS with P = 2.0 pu MW and Q = 0.5pu MVAR voltage of 0.98 per unit
which is below the scheduled or desired voltage magnitude. Assume that the generator on bus 1 is
operating at its maximum allowed var output.
Bus 2: SWING BUS with voltage 1.0 per unit at zero degrees phase angle
Bus 3: LOAD BUS sith P+jQ load of 4.0+0.9 puj
You may assume that the starting conditions for the powerflow has bus 1 with a voltage of 0.98
pu with zero degrees phase angle, and all other buses at 1.0 pu volts at zero degrees phase angle.
Work the entire problem in per unit.
A) Build the Y matrix for this system.
B) The bus voltage magnitudes and phase angles are the variables in a power flow. Which vari-
ables are known and which are unknown in this problem.
C) Tell which bus P and Q values are known and which are unknown for this problem.
D) Find the expression for the new or corrected voltage at bus 3 using the Gauss Seidel method.
Show all numerical values in this equation. Do not calculate the correction for any other buses.
2
G1
1
SWING
3LOAD
z12 = 0.1j
z23 = 0.3333j
z13 = 0.25j
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Problem 2 Part 1