<p style="text-align:justify"><span style="font-size:14px"><strong><u>Example 4.2:</u></strong> With reference to figure 4.12, calculate the fault currents for three-phase faults at buses A, B, C and D respectively. Also suggest the symmetrical breaking capacities of breakers 1, 2, 3 and 4. For a fault at bus C, what will be the fault current in 132 kV transmission line and fault current shared by each generator?</span></p>

<p style="text-align:justify">&nbsp;</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/16160610981616061098.jpg" style="height:524px; width:800px" /></span></p>

<p style="text-align:justify"><span style="font-size:14px"><strong><u>Solution:</u></strong> Base MVA =100 MVA</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(X_g=\frac{100}{82.35}\times 0.15\)</span>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; </span></p>

<p style="text-align:justify"><span style="font-size:14px">&nbsp;<span class="math-tex">\(Generator\hspace{0.1cm}MVA=\frac{70}{0.85}\)</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">\(=82.35\hspace{0.1cm}MVA\)</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;= 0.182 pu.</span></p>

<p style="text-align:justify"><span style="font-size:14px">pu reactance of 100 MVA generator transformers,</span></p>

<p style="text-align:justify"><span style="font-size:14px">X<sub>T1</sub> = 0.12 pu.</span></p>

<p style="text-align:justify"><span style="font-size:14px">Resistance and reactance of 132 kV transmission line,</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(pu\hspace{0.1cm}R_{T1}=\frac{100}{132^2}\times 3=0.017\hspace{0.1cm}pu \\ \)</span></span></p>

<p style="text-align:justify"><span class="math-tex">\(pu\hspace{0.1cm}X_{T1}=\frac{100}{132^2}\times 12=0.069\hspace{0.1cm}pu\)</span></p>

<p style="text-align:justify"><span style="font-size:14px">pu reactance of 50 MVA transformer on 100 MVA base,</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(X_{T2}=\frac{100}{50}\times 0.1=0.2\hspace{0.1cm}pu\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">Resistance and reactance of 66 kV transmission line on 100 MVA base,</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(pu\hspace{0.1cm}R_{T2}=\frac{100}{66^2}\times 2=0.046\hspace{0.1cm}pu \\ \)</span></span></p>

<p style="text-align:justify"><span class="math-tex">\(pu\hspace{0.1cm}X_{T2}=\frac{100}{66^2}\times 6=0.1377\hspace{0.1cm}pu\)</span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">Referring to reactance diagram shown in figure 4.13,</span></p>

<p style="text-align:justify">&nbsp;</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/16160611241616061124.jpg" style="height:524px; width:800px" /></span></p>

<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"><span class="math-tex">\(Fault\hspace{0.1cm}MVA=\frac{Base\hspace{0.1cm}MVA}{pu\hspace{0.1cm}Z}=\frac{100}{0.151}\)</span></span></p>

<p style="text-align:justify">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<span style="font-size:14px"><span class="math-tex">\(=662.25\hspace{0.1cm}MVA\)</span></span></p>

<p><span style="font-size:14px">Fault current, <span class="math-tex">\(I_f=\frac{662.25\times 10^3}{\sqrt3\times 132}\)</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; <span class="math-tex">\(=2896.6\hspace{0.1cm}Amp\)</span>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; </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></p>

<p style="text-align:justify">&nbsp;</p>

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

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(Fault\hspace{0.1cm}MVA=\frac{100}{0.017+j\hspace{0.1cm}0.22}\)</span></span></p>

<p style="text-align:justify">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<span class="math-tex">\(=\frac{100}{0.22\angle85.58}\)</span> &nbsp;</p>

<p style="text-align:justify">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<span class="math-tex">\(=454.55\angle-85.58^0\hspace{0.1cm}MVA\)</span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(I_f=1988\angle-85.58^0\hspace{0.1cm}Amp\)</span></span></p>

<p style="text-align:justify">&nbsp;</p>

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

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(Fault\hspace{0.1cm}MVA=\frac{100}{0.017+j\hspace{0.1cm}0.42}\)</span></span></p>

<p style="text-align:justify">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <span class="math-tex">\(=\frac{100}{0.42\angle87.68}\)</span>&nbsp;</p>

<p style="text-align:justify">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<span class="math-tex">\(=238.09\angle-87.68^0\hspace{0.1cm}MVA\)</span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(I_f=\frac{238.09\angle-87.68\times10^3}{\sqrt3\times66}\)</span></span></p>

<p style="text-align:justify">&nbsp; &nbsp; &nbsp;<span class="math-tex">\(=2082.79\angle-87.68^0\hspace{0.1cm}Amp\)</span></p>

<p style="text-align:justify"><span style="font-size:14px">For the same fault, fault current in primary of 50 MVA transformer (or in 132 kV line),</span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(I_{f132}=\frac{2082.79}{2}=1041.4\hspace{0.1cm}Amp\)</span></span></p>

<p style="text-align:justify">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">This fault current when shared by each generator can be calculated as follows:</span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">I<sub>f</sub> shared by each generator <span class="math-tex">\(=1041.4\times\frac{132}{11}\times\frac{1}{2}\)</span>&nbsp;</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; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 6248.4 Amp.</span></p>

<p style="text-align:justify">&nbsp;</p>

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

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(Fault\hspace{0.1cm}MVA=\frac{100}{0.063+j\hspace{0.1cm}0.5577}\)</span></span></p>

<p style="text-align:justify">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<span class="math-tex">\(=\frac{100}{0.561\angle83.55}\)</span> &nbsp;</p>

<p style="text-align:justify">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<span class="math-tex">\(=178.25\angle-83.55^0\hspace{0.1cm}MVA\)</span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">I<sub>f </sub>=1559.31 Amp.</span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">Symmetrical breaking capacities will be decided based on the fault MVA at the bus near the breaker.</span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">Therefore, symmetrical breaking capacity required for</span></p>

<ul>
	<li style="text-align:justify">
	<p><span style="font-size:14px">Breaker 1: 750 MVA</span></p>
	</li>
	<li style="text-align:justify">
	<p><span style="font-size:14px">Breaker 2: 500 MVA</span></p>
	</li>
	<li style="text-align:justify">
	<p><span style="font-size:14px">Breaker 3: 300 MVA</span></p>
	</li>
	<li style="text-align:justify">
	<p><span style="font-size:14px">Breaker 4: 200 MVA</span></p>
	</li>
</ul>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">Rounded off values are selected.</span></p>