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Direct Current vs. Alternating Current

A 10 MVA, 13....

Question

A 10 MVA, 13.8 kV alternator has positive, negative and zero sequence reactances of 30%, 40% and 5% respectively. The value of resistance that must be placed in the generator neutral so that the fault current for a LG fault of zero fault impedance will not exceed the rated line current is ________ $Ω$ .
18.43

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Solution

The correct option is A 18.43
Let base MVA be 10 MVA,

base kV = 13.8 kV

$E_{a} = (1 + j 0) p . u$

$Z_{B} = \frac{(13.8)^{2}}{10} = 19.044 Ω$

$I_{f} = \frac{3 E_{a}}{Z_{1} + Z_{2} + Z_{0} + 3 (Z_{n} + Z_{f})} = \frac{3 \times 1}{j (0.3 + 0.4 + 0.05) + 3 R_{n}} = 1$

$\Rightarrow \frac{3}{\sqrt{(0.75)^{2} + (3 R_{n}})^{2}} = 1$

$R_{n} = 0.9682 p . u$

$R_{n} = 18.439 Ω$

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