<p style="text-align:justify"><span style="font-size:14px"><strong>Example 6.1:<u> </u></strong>&nbsp;A 100 MVA, 132/66 kV, three-phase transformer is to be protected against short-circuit. An instantaneous overcurrent relay with setting range 400-2000 % (in steps of 50 %) of 1 amp is used for protection. The worst magnetizing inrush current of the transformer is 10 times the full load rated current. C. T. ratio is 500/1 amp. Suggest the setting of a relay.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><strong>Solution:</strong> Refer figure 6.11. The relay setting must be higher than possible magnetizing inrush as inrush decays after 15-30 cycles and instantaneous overcurrent relay operates in less than 3 cycles. (As we shall discuss later, it is possible to set numerical relay at a value less than this possibility of magnetizing inrush and hence offers much better protection particularly in case of very hazardous internal faults within the transformer.)</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/16251272801625127280.jpg" style="height:415px; width:800px" /></span></p>

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

<p style="text-align:justify"><span style="font-size:14px">Rated current of transformer&nbsp;</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(=\frac{100\times10^3}{\sqrt3\times132}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(=437.38\hspace{0.3cm}amp.\)</span></span></p>

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

<p style="text-align:justify"><span style="font-size:14px">Worst magnetizing inrush occurs when the transformer is energized at instantaneous value of voltage equal to zero in a. c. cycle and transformer is unloaded. </span></p>

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

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

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(=10\times437.38\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(=????4373.86\hspace{0.1cm}amp.\)</span></span></p>

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

<p style="text-align:justify"><span style="font-size:14px">C. T. secondary equivalent of this current,</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(=\frac{4373.86}{500}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">= 8.74 amp or 874&nbsp;% of&nbsp;&nbsp;1 amp.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">Therefore, Relay setting equal to 900 % of 1 amp is suggested, as the setting should be higher than the current due to magnetizing inrush in the next available 50 % step.</span></p>

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