181
(c)
The voltage regulation of the transmission line is
10000
8000
VR
100%
100%
25%
8000
S
R
R
V
V
V
−
−
=
×
=
×
=
Problems 98 through 910 refer to a single phase, 8 kV, 50Hz, 50 kmlong underground cable consisting of two
aluminum conductors with a 3 cm diameter separated by a spacing of 15 cm.
98.
The singlephase transmission line referred to in Problems 93 through 97 is to be replaced by an
underground cable.
The cable consists of two aluminum conductors with a 3 cm diameter, separated by a
centertocenter spacing of 15 cm.
As before, assume that the 50 Hz ac resistance of the line is 5% greater
than its dc resistance, and calculate the series impedance and shunt admittance of the line in ohms per km
and siemens per km.
Also, calculate the total impedance and admittance for the entire line.
S
OLUTION
The series inductance per meter of this transmission line is given by Equation (922).
1
ln
H/m
4
D
l
r
µ
π
§
·
=
+
¨
¸
©
¹
(922)
where
7
0
4
10
H/m
µ
µ
π
−
=
=
×
.
7
6
0
1
0.15 m
4
10
H/m
1
0.15 m
ln
ln
1.021
10
H/m
4
0.015 m
4
0.015 m
l
µ
π
π
π
−
−
×
§
·
§
·
=
+
=
+
=
×
¨
¸
¨
¸
©
¹
©
¹
Therefore the inductance of this transmission line will be
(
)
(
)
6
1.021
10
H/m
50,000 m
0.0511 H
L
−
=
×
=
The inductive reactance of this transmission line is
(
)(
)
2
2
50 Hz
0.0511 H
16.05
X
j
L
j
fL
j
j
ω
π
π
=
=
=
=
Ω
The resistance of this transmission line is the same as for the overhead transmission line calculated
previously:
AC
2.1
R
=
Ω
. The total series impedance of this entire line would be
2.1
16.05
Z
j
=
+
Ω
, so
the impedance per kilometer would be
(
) (
)
2.1
16.05
/
50 km
0.042
0.321
/km
Z
j
j
=
+
Ω
=
+
Ω
The shunt capacitance per meter of this transmission line is given by Equation (941).
ln
c
D
r
πε
=
§
·
¨
¸
©
¹
(941)
(
)
12
11
8.854
10
F/m
1.21
10
F/m
0.15
ln
0.015
c
π
−
−
×
=
=
×
§
·
¨
¸
©
¹
Therefore the capacitance per kilometer will be
8
1.21
10
F/km
c
−
=
×
The shunt admittance of this transmission line per kilometer will be
(
)
(
)
8
6
2
2
50 Hz
1.21
10
F/km
3.80
10
S/km
sh
y
j
fc
j
j
π
π
−
−
=
=
×
=
×
Therefore the total shunt admittance will be
(
)
(
)
6
4
3.80
10
S/km
50 km
1.90
10
S
sh
Y
j
j
−
−
=
×
=
×
99.
The underground cable is operating with the receiving side of the line opencircuited.
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 Fall '08
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 Alternating Current, Volt, iL, Electric power, Transmission line, Mains electricity, Di r

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