Question

A $3-\varphi$, 220 kV line operating at 50 Hz and conductors arranged as shown below, the conductor radius is 0.40 cm. The charging current per km is __________A

• A. 0.45

Answer 1

The correct option is A 0.45
The radius of conductor = 0.4 cm
The mutual GMD of conductor,
$D_m=\sqrt[3]{380\times 40\times 40}$
= 50.3968 = 50.4 cm

Capacitance per phase per meter
$=\frac{2\pi {ϵ}_0}{ın\frac{50.4}{0.4}}F/m$
$=\frac{2\pi \times 8.85\times {10}^{-12}}{4.836}=1.15\times {10}^{-11}F/m$
$=1.15\times {10}^{-8}F/km$
The charging current $=V\omega C=\frac{220}{\sqrt{3}}\times 1000\times 1.15\times 2\pi \times 50\times {10}^{-8}$
= 0.45889 A/km.