Electrical Power Systems

V Ki =
1
pÎ
N
å
q
m
2 o m = 1
3.3 CAPACITANCE O A SINGLE PHASE LINE
HG
Km
I
KJ
Capacitance of Transmission Lines 55
Dim
ln Volts ...(3.5)
D
igure 3.3 shows a single phase line consisting of two long solid conductors having raidus r 1 and
r 2 respectively. Conductor 1 carries a charge of q 1 coulombs/m and conductor 2 carries a charge
of q 2 coulombs/m. The field of the first conductor is disturbed due to the presence of the second
conductor and the ground. The distance between the conductors is D and D is much greater
than the raddi of the conductors. Also, the height of the conductors from the ground is much
larger than D. Therefore the effect of distortion is negligible and the charge is assumed to be
uniformly distributed.
ig. 3.3: Single phase two-wire line.
The potential difference V 12 can be obtained in terms of q 1 and q 2 by using eqn. (3.5). Thus,
V 12 =
\ V 12 =
1
2pÎ
1
2pÎ
2
å
q
m
o m = 1
o
L
NM
q
1
HG
D2mI
HG D1mKJ
ln Volt
I
HG
IO
KJQP
21
22
2
11KJ
12
+
D
D
ln q ln Volt ...(3.6)
D
D
Since q 2 = –q 1 , D 21 = D 12 = D, D 11 = r 1 and D 22 = r 2
V 12 =
1
2pÎ
o
L
NM
D r2
q1
ln - q1
ln Volt
r D
\ V12 = 2q1D
ln Volts
2 rr
\ C12 = q1
pÎ o
If r 1 = r 2 = r
\ C 12 =
1
12
p Îo
=
V D
12 ln
rr
o
I
HG r KJ
pÎ
ln D
12
O Q P
/m ...(3.7)
/m ...(3.8)