<p style="text-align:justify"><span style="font-size:14px"><strong><u>Example 4.1:</u></strong> Refer figure 4.10. Calculate the fault currents for three-phase faults at buses A, B, C, D and E. Ignore resistance of transmission lines.</span></p>

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<p style="text-align:justify"><span style="font-size:14px"><img alt="" src="https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16160599181616059918.jpg" style="float:left; height:515px; width:800px" /></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><strong><u>Solution:</u></strong>&nbsp;&nbsp;Base MVA = 150 MVA.</span></p>

<p style="text-align:justify"><span style="font-size:14px">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Base kV = 132 kV line to line.</span></p>

<p style="text-align:justify"><span style="font-size:14px">pu reactance of Generator = 0.2 pu on its own base</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(Generator\hspace{0.1cm}MVA=\frac{120}{0.85}=141.17\hspace{0.1cm}MVA\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">pu reactance of Generator referred to</span></p>

<p style="text-align:justify"><span style="font-size:14px">&nbsp;<span class="math-tex">\(150\hspace{0.1cm}MVA=\frac{MVA_{new}}{MVA_{old}}\times Z_{puold}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<span class="math-tex">\(=\frac{150}{141.17}\times 0.2=0.2125\hspace{0.1cm}pu\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">pu reactance of transformer = 0.1 pu.</span></p>

<p style="text-align:justify"><span style="font-size:14px">For transmission lines,</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(pu\hspace{0.1cm}X=\frac{MVA}{\left(KV\right)^2}\times Z_{ohm}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(pu\hspace{0.1cm}X_{AB}=\frac{150}{132^2}\times 6=0.0516\hspace{0.1cm}pu\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">Similarly,</span></p>

<p style="text-align:justify"><span style="font-size:14px"><em>pu X</em><sub><em>BC</em></sub>&nbsp;= 0.0344 pu</span></p>

<p style="text-align:justify"><span style="font-size:14px"><em>pu X</em><sub><em>CD</em></sub>&nbsp;= 0.0344 pu</span></p>

<p style="text-align:justify"><span style="font-size:14px"><em>pu X</em><sub><em>DE</em></sub>&nbsp;= 0.0344 pu</span></p>

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<p style="text-align:justify"><span style="font-size:14px">Referring to reactance diagram shown in figure 4.11,</span></p>

<p style="text-align:justify"><span style="font-size:14px"><img alt="" src="https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16160599561616059956.jpg" style="height:515px; width:800px" /></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><strong>For a three-phase fault at bus A,</strong></span></p>

<p style="text-align:justify"><span style="font-size:14px">Pu X = 0.15625 pu</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(Fault\hspace{0.1cm}MVA=\frac{Base\hspace{0.1cm}MVA}{pu\hspace{0.1cm}X}\)</span></span></p>

<p style="text-align:justify">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<span class="math-tex">\(=\frac{150}{0.15625}\)</span></p>

<p style="text-align:justify">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<span class="math-tex">\(=960\hspace{0.1cm}MVA\)</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(Fault\hspace{0.1cm}Current=\frac{960\times 10^6}{\sqrt3\times132\times 10^3}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<span class="math-tex">\(=4198.9\hspace{0.1cm}Amp\)</span></span></p>

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<p style="text-align:justify"><strong><span style="font-size:14px">Similarly, for fault at bus B,</span></strong></p>

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<p style="text-align:justify"><span style="font-size:14px">Pu X = 0.20785 pu.&nbsp;&nbsp;&nbsp;&nbsp; </span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(Fault\hspace{0.1cm}MVA=\frac{150}{0.20785}\)</span>&nbsp;</span></p>

<p style="text-align:justify">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<span class="math-tex">\(=721.67\hspace{0.1cm}MVA\)</span></p>

<p style="text-align:justify"><span style="font-size:14px">Fault Current = 3156.5 Amp.</span></p>

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<p style="text-align:justify"><span style="font-size:14px"><strong>For fault at bus C,</strong></span></p>

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<p style="text-align:justify"><span style="font-size:14px">Fault MVA = 619.195 MVA.&nbsp;&nbsp;&nbsp; Fault Current, I<sub>f</sub> = 2708.27 Amp.</span></p>

<p style="text-align:justify"><span style="font-size:14px">For fault at bus D,</span></p>

<p style="text-align:justify"><span style="font-size:14px">Fault MVA = 542.20 MVA.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></p>

<p style="text-align:justify"><span style="font-size:14px">I<sub>f</sub> = 2371.5 Amp.</span></p>

<p style="text-align:justify"><span style="font-size:14px">For fault at bus E,</span></p>

<p style="text-align:justify"><span style="font-size:14px">Fault MVA = 482.24 MVA.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></p>

<p style="text-align:justify"><span style="font-size:14px">I<sub>f</sub> = 2109.24 Amp</span></p>

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<p style="text-align:justify"><span style="font-size:14px">The reader shall note that while carrying out this fault analysis, pre-fault currents are not considered as usually the fault currents are much larger than the load currents. Hence, the load currents are ignored in comparison to the fault currents. The fault analysis considering the pre-fault currents, however, can be carried out, but it is little complicated. It is a usual practice to ignore the pre-fault currents.</span></p>

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