Identify the condition for resonance

For an arc suppression coil (Petersen coil) to compensate for the charging current, it must resonate with the system capacitance such that $\omega L = \frac{1}{3 \omega C}$.

$L = \frac{1}{3 \omega^2 C}$

Calculate the angular frequency

Given frequency $f = 50 \text{ Hz}$, the angular frequency is $\omega = 2 \pi f$.

$\omega = 2 \times \pi \times 50 = 314.16 \text{ rad/s}$

Calculate the capacitance from susceptance

The susceptance $B$ is given by $B = \omega C$. Thus, $C = \frac{B}{\omega} = \frac{4 \times 10^{-4}}{314.16} \text{ F}$.

$C = 1.273 \times 10^{-6} \text{ F}$

Calculate the inductance L

Substitute the values into the resonance formula: $L = \frac{1}{3 \times (314.16)^2 \times 1.273 \times 10^{-6}}$.

$L \approx 654 \text{ H}$