University of Zululand
Department of Engineering
Transmission Lines
5EEE322, 2024
Tutorial 2 –Transmission Lines: Steady State
Due Date:
Question 1
A 150-km, 230-kV, 60-Hz three-phase line has a positive-sequence series impedance z = 0.08
+ j0.48 Ώ/km and a positive-sequence shunt admittance y = j3.33 x 10-6 S/ km. At full load, the
line delivers 250 MW at 0.99 p.f. lagging and at 220 kV. Using the nominal π- circuit,
calculate;
a) ABCD parameters,
b) Sending-end voltage and current,
c) Percent voltage regulation,
d) The efficiency of the line,
e) The maximum theoretical power that can be transferred by the line.
Question 2
A three-phase, 765 kV 60 Hz, 400 km long lossless line transmission has the following ABCD
parameters:
A= cos 𝛽𝑙 = cos 29° = 0.8746
B = 𝑗𝑍𝑐 sin 𝛽𝑙 = 𝑗264.7 sin 29° = 𝑗128.33
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C=𝑗 1
sin 𝛽𝑙 = 𝑗
sin 29° = 𝑗0.00183𝑆
264.7
𝑍𝑐
D=A
Where β is the phase constant, L is the line length, and 𝑍𝑐is the surge impedance.
a) Determine the wavelength λ and the surge impedance loading (SIL).
b) The line energized with 765 kV at the sending end when the load at the receiving-end
is removed. Find the receiving-end voltage.
Question 3
i) The inductive reactance of an underground high-voltage ac line is much smaller than its
capacitive reactance. For a given voltage level, the Surge Impedance Loading (SIL) of an
underground cable is (choose the correct answer)
a) Equal to the SIL of an overhead line
b) Smaller than the SIL of an overhead line
c) Bigger than the SIL of an overhead line
ii) For a lossless line, the surge impedance 𝑍𝑐 is purely resistive. Under Surge Impedance
Loading (SIL), the voltage and current at any point along the line are constant in
magnitude and are equal to their sending end values. For this condition, the reactive power
absorbed by line is (choose the correct answer)
a) Bigger than the reactive power generated by the line
b) Smaller than the reactive power generated by the line
c) Equal to the reactive power generated by the line
iii) State whether the following statement is true (T) or false (F)
If the magnitudes of the sending end and the receiving end voltage of a lossless
transmission line are maintained the same, the reactive power absorbed by the line
is supplied by both ends.
Question 4
A two-conductor, single phase short line has a total resistance of 0.4 Ω and a total inductive
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reactance of 0.15 Ω. The line supplies a load of 100 A at 400 V and 0.8 p.f. lagging. Calculate
a) The sending-end voltage
b) The per unit regulation
c) The transmission efficiency
Question 5
The equations of two port networks are given as follows.
𝑉
𝑉
𝐴 𝐵1 𝑉𝑅1
𝐴 𝐵2 𝑉𝑅2
[ 𝑠1 ] = [ 1
] [ ], [ 𝑠2 ] = [ 2
][ ]
𝐼𝑠1
𝐼𝑠2
𝐶1 𝐷1 𝐼𝑅1
𝐶2 𝐷2 𝐼𝑅2
a) What are the equivalent parameters of the two networks connected in series?
b) If they are connected in parallel, what are equivalent ABCD parameters?
c) Using the results obtained, calculate the ABCD parameters of the two Pi
networks connected in series and in parallel.
Question 6
A three-phase, 60 Hz , 500 kV is 300 km. The line inductance is 0.97 mH/km per phase and
its capacitance is 0.0115 µF/km per phase.
(a) Determine the line phase constant 𝛽, the surge impedance Zc, the velocity of
propagation v and the line wavelength λ.
(b) If the line supplies a load of 1000 MVA, 0.8 power factor lagging at 500kV,
determine the MVAr and the capacitance of the shunt capacitor to be installed at the
receiving end to keep the receiving end voltage at 500 kV when the line is energized
with 500 kV at the sending end.
(c) If only series capacitors are installed at the midpoint of the line providing 40%
compensation, find the sending end voltage and voltage regulation.
Question 7
A 60-Hz, 230-km, three-phase overhead transmission line has a series impedance
𝑧 = 0.8432 ∠79.04° Ω/km and shunt admittance, = 5.105 × 10−6∠90° S/km. The load at the
receiving end is 125 MW at unity power factor and a voltage of 215 kV. Determine the voltage,
current, real and reactive power at the sending end and the percent voltage regulation of the
line.
Question 8
A three-phase power of 700 MW is to be transmitted to a substation located 315 km from the
source power. For a preliminary line design assume the following parameters:
VS = 1.0 p.u., VR = 0.9 p.u, l = 5000 km, Zc = 320 and  = 36.87
a) Based on the practical line loadability equation determine a nominal voltage level for
the transmission line.
b) For the transmission voltage level obtained in (a), calculate the theoretical maximum
power that can be transferred by the transmission line.
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