Electrical Power Systems

Resistance and Inductance of Transmission Lines 41
\ X L = Lw = 0.904 × 10 –3 × 2p × 50 W/km = 0.284 W/km
Example 2.8: Determine the geometric mean radius of a conductor in terms of the radius r of
an individual strand for (a) three equal strands as shown in ig. 2.19(a) and (b) four equal
strands as shown in ig. 2.19(b).
Solution:
ig. 2.19 (a) ig. 2.19 (b)
(a) D s = (r¢ · 2r · 2r) 1/3 = r(0.7788 × 4) 1/3 = 1.46 r
1/ 4
e j = 1.722 r
(b) Ds = (r¢ · 2r ·2r · 2 2r) 1/4 = r 0. 7788 ´ 8 2
Example 2.9: A three-phase untransposed transmission line and a telephone line are supported
on the same towers as shown in ig. 2.20. The power line carries a 50 Hz balanced current of 150
Amp per phase. The telephone line is located directly below phase C. ind the voltage per km
induced in the telephone line.
Solution:
D
D
b2
b1
2 2
= (.) 4 6 + 4 = 6. 096 m
2 2
= (.) 34 + 4 = 525 .
m
U
V|
W|
ig. 2.20
D
D
a2
a1
2 2
= (.) 8 6 + 4 = 9. 484 m
2 2
= (.) 74 + 4 = 841 .
rom ig. 2.20, the flux linkage between conductors T 1 and T 2 due to current I a is
HG
l12(Ia) = 0.4605 Ia log Da2
D
a1
I
KJ mWb–T/km
The flux linkage between conductors T 1 and T 2 due to current I b is
m
U
V|
W|