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Single Line to Ground (L-G) Fault - Unloaded & Loaded

A three phase...

Question

A three phase, 200 MVA, 11 kV generator has the following p.u. constants. The generator neutral is solidly grounded $X_{1} = X_{2} = 3 X_{0} = 0.30 Ω$ . The ratio of the fault current due to three phase dead short circuit to that of L-G fault would be _____.
0.78

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Solution

The correct option is A 0.78
$I_{f 3 - ϕ} = \frac{E_{f}}{X_{1}}$

$I_{f L - G} = \frac{3 E_{f}}{X_{1} + X_{2} + X_{0}}$

$\frac{I_{f 3 - ϕ}}{I_{f L - G}} = \frac{X_{1} + X_{2} + X_{0}}{3 X_{1}}$

$= \frac{0.30 + 0.30 + 0.10}{3 \times 0.30} = 0.778 \approx 0.78$

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