Question

A 220 kV, 50 Hz, 50 km single phase line, consisting of two parallel wires each 6 mm in diameter and 2 m apart. Then the charging current (in Ampere) is

• A. 8.52
• B. 29.56
• C. 14.76
• D. 17.047

Answer 1

The correct option is B 29.56

Capacitance per meter length,

$C_N=\frac{2\pi {\epsilon }_0}{ln\frac{D}{r}}F/m=\frac{2\pi \times 8.854\times {10}^{-12}}{ln\left(\frac{2}{3\times {10}^{-3}}\right)}=8.555\times {10}^{-12}$ F/m

$C_N=8.555\times {10}^{-3}\mu F/km$
$C_N$ of 50 km line = 0.4277 $\mu$F

Charging current $=\frac{V}{X_C}=V\omega C=220\times {10}^3\times 2\pi \times 50\times 0.4277\times {10}^{-6}$
I = 29.56 A