Statement- For a power system the admittance and impedance matrices for the fault studies are follows-Ybus- -j8-75 j1-25 j2-50- j1-25 -j6-25 j2-50- j2-50 j2-50 -j5-00 -Zbus- j0-16 j0-08 j0-12- j0-08 j0-24 j0-16- j0-12 j0-16 j0-34 -The pre-fault voltages are 1-0 p-u- at all the buses- The system was unloaded prior to the fault- A solid 3 phase fault takes place at bus 2-Q- The post fault voltages at buses 1 and 3 in per unit respectively are

Pre fault V_BUS=[ V_1^0; V_2^0; V_3^0 ]=[ 1∠ 0^∘; 1∠ 0^∘; 1∠ 0^∘ ] Fault current =I_f=V_r^0Z_rr+Z_f Solid 3 ϕ fault occurs at bus 2, r = 2 and nbsp; Z_F=0 ...

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Power Systems

Y-Bus with Mutual Reactance

Statement: Fo...

Question

Statement:
For a power system the admittance and impedance matrices for the fault studies are follows.

$Y_{b u s} = ⎡ ⎢ ⎣ \begin{matrix} - j 8.75 & j 1.25 & j 2.50 j 1.25 & - j 6.25 & j 2.50 j 2.50 & j 2.50 & - j 5.00 \end{matrix} ⎤ ⎥ ⎦$

$Z_{b u s} = ⎡ ⎢ ⎣ \begin{matrix} j 0.16 & j 0.08 & j 0.12 j 0.08 & j 0.24 & j 0.16 j 0.12 & j 0.16 & j 0.34 \end{matrix} ⎤ ⎥ ⎦$

The pre-fault voltages are 1.0 p.u. at all the buses.
The system was unloaded prior to the fault. A solid 3 phase fault takes place at bus 2.

Q: The post fault voltages at buses 1 and 3 in per unit respectively are

0.24, 0.63

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0.31, 0.76

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0.33, 0.67

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0.67, 0.33

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Solution

The correct option is D 0.67, 0.33
$P r e f a u l t V_{B U S} = ⎡ ⎢ ⎢ ⎣ \begin{matrix} V_{1}^{0} V_{2}^{0} V_{3}^{0} \end{matrix} ⎤ ⎥ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 ∠ 0^{\circ} 1 ∠ 0^{\circ} 1 ∠ 0^{\circ} \end{matrix} ⎤ ⎥ ⎦$

$F a u l t c u r r e n t = I_{f} = \frac{V_{r}^{0}}{Z_{r r} + Z_{f}}$
Solid $3 - ϕ$ fault occurs at bus 2, r = 2 and

$Z_{F} = 0$

$Z_{r r} = Z_{22} = j 0.24,$

$V_{r}^{0} = V_{1}^{0} = 1 ∠ 0^{\circ}$

$I_{f} = \frac{V_{2}^{0}}{Z_{22} + Z_{f}} = \frac{1 ∠ 0^{\circ}}{j 0.24 + 0} = - j 4.167 p . u .$

Post fault voltage at bus i is given by
$V_{i}^{f} = V_{i}^{0} - Z_{i r} I_{f}$

Post fault voltage at bus, $i = 1$

$V_{1}^{f} = V_{1}^{0} - Z_{12} I_{f}$

$= 1 ∠ 0^{\circ} - j 0.08 \times (- j 4.167)$

$= 0.67 p . u .$

Post fault voltage at bus , i = 3
$V_{3}^{f} = V_{3}^{0} - Z_{32} I_{f}$

$= 1 ∠ 0^{\circ} - j 0.16 \times (- j 4.167) = 0.33 p . u .$

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Similar questions

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