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RLC Circuit

A 3ϕ SC occur...

Question

A $3 ϕ$ SC occurs at BUS -4. The SC current flowing between buses 1 and 2 is ___
Assume that the pre fault voltage at all the buses is 1.0 Pu.

$Z_{b u s} = j ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 0.15 & 0.08 & 0.04 & 0.07 0.08 & 0.15 & 0.06 & 0.09 0.04 & 0.06 & 0.13 & 0.05 0.07 & 0.09 & 0.05 & 0.12 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦$

A

- 2.13 ∠ 90^{o}

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B

2.13 ∠ - 90^{o}

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C

4.08 ∠ - 90^{o}

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D

- 4.08 ∠ - 90^{o}

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Solution

The correct option is B $2.13 ∠ - 90^{o}$
Before Fault:
$V_{1}^{'} = 1.0, V_{2}^{'} = 1.0, V_{3}^{'} = 1.0, V_{4}^{'} = 1.0 I_{f} = I_{4} = \frac{V_{4}^{'}}{Z_{44}} = \frac{1.0}{j 0.12} = - j 8.33$

During fault:
$V_{1}^{'} = I_{f} Z_{14} = I_{4} Z_{14} = 0.58 V_{2}^{'} = I_{f} Z_{24} = I_{4} Z_{24} = 0.75$

$Z_{14} = j 0.04$
$Z_{24} = j 0.09$

The SC current flowing between buses 1 and 2 is

$I_{12} = \frac{(V_{1}^{'} - V_{2}^{'})}{Z_{12}} = \frac{(0.58 - 0.75)}{j 0.08} = 2.13 ∠ - 90^{o}$

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