Question

Repeat Problem 11.10, except assume there is a three-phase-to-ground bolted short circuit at bus five.

Short answer

The Thevenin equivalent reactance of the system is $j0.03142\text{\hspace{0.33em}pu}$.

Step-by-step solution

Write the data given from the question.

The reactance between the line 2-4, $X_{42}=j0.100\text{\hspace{0.33em}pu}$

The reactance between the line 2-5,$X_{25}=j0.050\text{\hspace{0.33em}pu}$

The reactance between the line 4-5,$X_{45}=j0.025\text{\hspace{0.33em}pu}$

The reactance between the line 1-5,$X_{15}=j0.02\text{\hspace{0.33em}pu}$

The reactance between the line 3-4,$X_{34}=j0.01\text{\hspace{0.33em}pu}$

Determine the Thevenin’s equivalent reactance from three terminal.

Consider the single line diagram of the system

The equivalent reactance of the system is given by as follows.

$X_{Th}=X_{{}_{34}}+\left[X_{45}\parallel \left(X_{42}+X_{25}\right)\right]$

Substitute $j0.100\text{\hspace{0.33em}pu}$ for X₄₂, $j0.050\text{\hspace{0.33em}pu}$ for X₂₅, $j0.025\text{\hspace{0.33em}pu}$ for X₄₅ and $j0.01\text{\hspace{0.33em}pu}$for X₃₄ into above equation.

$\begin{array}{c}{X}_{Th}=j0.01+\left[j0.025\parallel \left(j0.10+j0.05\right)\right]\\ X_{Th}=j0.01+j\left(0.025\parallel 0.15\right)\\ X_{Th}=j0.01+j0.02142\\ X_{Th}=j0.03142\text{\hspace{0.33em}pu}\end{array}$

Hence, the Thevenin equivalent reactance of the system is $j0.03142\text{\hspace{0.33em}pu}$.