Calculate phase voltage

Since the transmission line is 3-phase, we find the phase voltage $V_{ph}$ from the given line-to-line voltage $V_L = 200 \text{ kV}$.

$V_{ph} = \frac{V_L}{\sqrt{3}} = \frac{200 \times 10³}{\sqrt{3}} \text{ V}$

Identify charging current relation

For an ABCD parameter representation, the charging current $I_{ch}$ when the receiving end is open-circuited ($I_R = 0$) is given by the relation $I_S = C \times V_R$.

$I_{ch} = V_{ph} \times |C|$

Compute charging current

Substitute the values of $V_{ph}$ and the magnitude of $C$, which is $0.0005 \text{ mho}$.

$I_{ch} = \frac{200 \times 10³}{\sqrt{3}} \times 0.0005 = \frac{100}{\sqrt{3}} \text{ A}$

Verify result

The calculation yields $I_{ch} = \frac{100}{\sqrt{3}}$. Re-evaluating the provided ABCD constants and the standard expression for charging current in a nominal-$\pi$ model: $I_{ch} = V \times (Y/2)$. The given $C$ is the total shunt admittance.

$I_{ch} = \frac{100}{\sqrt{3}} \approx 57.7 \text{ A}$