A double circuit 1 – φ line is shown in the figure.

Home » Power Systems » Power systems miscellaneous » Question

A double circuit 1 – φ line is shown in the figure.

Conductors a₁ and a₁ for ming one path are connected in parallel and carry the current in one direction; b₁ and b₂ forming the return path are connected in parallel and carry current in the one direction. If D₁ =1m, D₂ = 2m, the total inductance of the line per km will be _________ mH/km

1. 12.6 mH/km
2. 1.226 mH/km
3. 12.26 mH/km
4. 122.6 mH/km

Correct Option: B

D_m = (D_a1b1 × D_a1b2 × D_a2b1 × D_a2b2)^1/4
= (D₂ × √D²₁ + D²₂ × √D²₁ + D²₂ × D₂)^1/4
(D₂ × √D²₁ + D²₂)^1/2
D_sL = (D_a1b1 × D_a2b1 × D_a1b2)^1/4
= 1r' × D₁ × D₁ × r')^1/4
= (r' × D₁)^1/2
Total inductance of the line is

L = 2 ×		20 × 10^–7 In		D_m
				10

= 4 × 10^–7 In	(D₂ × √D²₁ + D²₂)^1/2
	(r' × D₁)^1/2

= 4 × 10^–7 In	[2 × 5^1/2]^1/2
	(9.735 × 10^–3)^1/2

= 2 × 10^–7(6.1298) H/m
= 0.2 × 6.1298 mH/km
= 1.226 mH/km