<p style="text-align:justify"><span style="font-size:14px"><strong><u>Example 4.4:</u></strong> Consider a three-bus system of figure 4.16. Both the generators are 120 MW, 0.85 pf each with transient reactance 15 %. Both the transformers are of 150 MVA capacity with equivalent leakage reactance 10 % each. Calculate the fault current for a three-phase fault as shown in figure. Assume all line reactances are given on 150 MVA base.</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/16194186601619418660.jpg" style="height:675px; width:800px" /></span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><strong><u>Solution:</u> </strong>The reactance diagram of figure 4.16 is as shown in figure 4.17. </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/16160621251616062125.jpg" style="height:675px; width:800px" /></span></p>

<p style="text-align:justify"><span style="font-size:14px">Base MVA = 150.</span></p>

<p style="text-align:justify"><span style="font-size:14px">Generator reactance at 150 MVA base,</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(=\frac{150\times 0.85}{120}\times 0.15=0.1594\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">Now, for further analysis, delta to star transformation is required. The reactances in star formation are each equal with values</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(\frac{0,1\times 0.1}{0.1+0.1+0.1}=0.03333\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">The reactance diagram after delta to star conversion is given in figure 4.18.</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/16160621551616062155.jpg" style="height:675px; width:800px" /></span></p>

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

<p style="text-align:justify"><span style="font-size:14px">X<sub>eq</sub> = 0.18 pu.</span></p>

<p style="text-align:justify"><span style="font-size:14px">Fault MVA &nbsp;<span class="math-tex">\(=\frac{150}{0.18}\)</span>&nbsp;=834.75 MVA.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(I_f=\frac{834.75\times 10^3}{\sqrt3\times 132}=3651\hspace{0.1cm}Amp\)</span></span></p>