<p style="text-align:justify"><img alt="" src="https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16253847621625384762.jpg" style="height:528px; width:900px" /></p>

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

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

<p style="text-align:justify"><span style="font-size:14px"><strong><u>Example 3:</u></strong> Figure 7.16 shows a power system network. Ground relays R<sub>1</sub>, R<sub>2</sub> and R<sub>3</sub> are normal inverse IDMT relays with inbuilt high-set instantaneous units. The % overreach of instantaneous units of relays is 10 %. The fault currents are tabulated below:</span></p>

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

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

<table cellspacing="0" class="MsoTableGrid" style="border-collapse:collapse; border:none; margin-left:57px; width:900px">
	<caption>
	<p><strong><span style="font-size:18px">Table 7.7: Fault Currents at Different Buses</span></strong></p>
	</caption>
	<tbody>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; vertical-align:top; width:94px">
			<div style="text-align:center"><span style="font-size:28px">Fault at Bus</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:top; width:114px">
			<div style="text-align:center"><span style="font-size:28px">Fault Current for L-L-L-g Fault in Amp</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:top; width:123px">
			<div style="text-align:center"><span style="font-size:28px">Fault Current for L-L Fault in </span></div>

			<div style="text-align:center"><span style="font-size:28px">Amp</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:top; width:113px">
			<div style="text-align:center"><span style="font-size:28px">Fault Current for L-g Fault in Amp</span></div>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:20px; vertical-align:top; width:94px">
			<div style="text-align:center"><span style="font-size:28px">A</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:20px; vertical-align:top; width:114px">
			<div style="text-align:center"><span style="font-size:28px">3131</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:20px; vertical-align:top; width:123px">
			<div style="text-align:center"><span style="font-size:28px">2711</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:20px; vertical-align:top; width:113px">
			<div style="text-align:center"><span style="font-size:28px">3859</span></div>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:20px; vertical-align:top; width:94px">
			<div style="text-align:center"><span style="font-size:28px">B</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:20px; vertical-align:top; width:114px">
			<div style="text-align:center"><span style="font-size:28px">2094</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:20px; vertical-align:top; width:123px">
			<div style="text-align:center"><span style="font-size:28px">1813</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:20px; vertical-align:top; width:113px">
			<div style="text-align:center"><span style="font-size:28px">2024</span></div>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; vertical-align:top; width:94px">
			<div style="text-align:center"><span style="font-size:28px">C</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:114px">
			<div style="text-align:center"><span style="font-size:28px">2144</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:123px">
			<div style="text-align:center"><span style="font-size:28px">1856</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:113px">
			<div style="text-align:center"><span style="font-size:28px">2560</span></div>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; vertical-align:top; width:94px">
			<div style="text-align:center"><span style="font-size:28px">D</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:114px">
			<div style="text-align:center"><span style="font-size:28px">1602</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:123px">
			<div style="text-align:center"><span style="font-size:28px">1388</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:113px">
			<div style="text-align:center"><span style="font-size:28px">1676</span></div>
			</td>
		</tr>
	</tbody>
</table>

<p>&nbsp;</p>

<p>&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">Determine P. S., TMS and setting of high-set instantaneous units of ground relays R<sub>1</sub>, R<sub>2</sub> and R<sub>3</sub>. Also suggest setting of high-set instantaneous units of phase relays R<sub>1</sub>, R<sub>2</sub> and R<sub>3</sub>. Assume setting range of ground relays as 10-40 % of 1 amp and excitation current of all CTs as 0.05 amp.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><strong><u>Solution:</u></strong>&nbsp; TMS of R<sub>3</sub> = 0.1 (minimum, assumed)</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">TMS of R<sub>2</sub> = 0.1 (as settings of R<sub>2</sub> and R<sub>3</sub> are independent, ground relay R<sub>2</sub> is not to be graded with ground relay R<sub>3</sub> as delta-wye transformer is there between these two relays).</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">P. S. of R<sub>3</sub> = 10 % (minimum available). As there is delta-wye transformer intervening between relaying points R<sub>2</sub> and R<sub>3</sub>, these relays are not required to be coordinated and can be independently set. Therefore, P. S. of R<sub>2</sub> =10 % (minimum available).</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(\dot{.\hspace{0.095in}.}P.S.of\hspace{0.1cm}R_1\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(&gt;\frac{1.3}{1.05}\times P.S.\hspace{0.1cm}of\hspace{0.1cm}R_2\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(&gt;92.85\)</span>&nbsp;amp (prime)</span></p>

<p style="text-align:justify"><span style="font-size:14px">&gt; 0.3095 amp (sec of <span class="math-tex">\(\frac{300}{1}\)</span>&nbsp;CT).</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">P. S. of R<sub>2</sub> in CT primary terms = 300 [0.1 + 3(0.05)] =75 amp.</span></p>

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

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

<p style="text-align:justify"><span style="font-size:14px">Therefore, current through R<sub>1</sub> = 0.3095 &ndash; 0.15 = 0.1595 amp = 15.95 % 0f 1 amp. Hence, P. S. of R<sub>1</sub> is selected as 20 %.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><u>Settings of high-set Instantaneous units of ground relays:</u></span></p>

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

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

<p style="text-align:justify"><span style="font-size:14px">Setting of H. S. unit of ground relay R<sub>3&nbsp;</sub></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(= \frac{100\times B}{100-A}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(=\frac{100\times \frac{1676}{300}}{100-10}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">= 6.2 amp, or 620% of 1 amp.Hence, high-set setting of 650 % selected.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">Setting of H. S. unit of ground relay R<sub>2</sub></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(=\frac{100\times \frac{2560\times66}{\sqrt3\times132\times300}}{90}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">= 2.73 amp, or 273% of 1 amp.&nbsp;Hence H. S. setting of 400 % (minimum available) is selected.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">Setting of H. S. unit of R<sub>1</sub></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(= \frac{100\times \frac{2024}{300}}{90}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">= 7.40 amp or 749% of 1 amp.&nbsp;Hence, H. S. setting 750 % suggested.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><strong><u>R<sub>1</sub>-R<sub>2</sub> coordination:</u></strong> I<sub>f</sub> = 2024 amp, i<sub>f</sub> (secondary equivalent) = 6.746 amp. Current through the ground relay R<sub>2</sub> will be equal to (6.746 &ndash; 0.15) 6.6 amp, or 660 % of 1 amp. This is more than high-set setting 400 %. Hence R<sub>2</sub> will operate within 0.06 sec (maximum). Therefore, Top of R<sub>1</sub> = 0.06 + .25 = 0.31 sec.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">Hence TMS of R<sub>1</sub></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(=\frac{0.31\times log_{10}20}{3}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">=0.1344,&nbsp;<em>hence 0.15 selected.</em></span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><u>High-set Settings of Phase Overcurrent Relays:</u></span></p>

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

<p style="text-align:justify"><span style="font-size:14px">H. S. Setting of R<sub>3</sub></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(=\frac{100\times \frac{1602}{300}}{90}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">= 5.93 amp or 593% of 1 amp, hence 600 % selected.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">H. S. Setting of R<sub>2</sub> &nbsp;</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(=\frac{100\times \frac{2144\times 66}{132\times 300}}{90}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">= 3.97 amp or 397 % of 1 amp, hence 400 % selected.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">H. S. Setting of R<sub>2</sub> </span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(=\frac{100\times \frac{2094}{300}}{90}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">= 7.75 amp or 775 % of 1 amp, hence 800% suggested.</span></p>

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

<table cellspacing="0" class="MsoTableGrid" style="border-collapse:collapse; border:none; width:900px">
	<caption>
	<p><strong><span style="font-size:18px">Table 7.8: Summary of Settings of Relays of Example 3</span></strong></p>
	</caption>
	<tbody>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; vertical-align:top; width:120px">
			<div style="text-align:center"><strong><span style="font-size:28px">Relay</span></strong></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:top; width:120px">
			<div style="text-align:center"><strong><span style="font-size:28px">P. S. of Ground Relay in % of 1 amp</span></strong></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:top; width:120px">
			<div style="text-align:center"><strong><span style="font-size:28px">TMS of Ground Relay</span></strong></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:top; width:120px">
			<div style="text-align:center"><strong><span style="font-size:28px">H. S. Inst. Setting of Ground Relay in % of 1 amp</span></strong></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:top; width:120px">
			<div style="text-align:center"><strong><span style="font-size:28px">H. S. Inst. Setting of Phase Relays in % of 1 amp</span></strong></div>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">R<sub>1</sub></span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">20</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">0.15</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">750</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">800</span></div>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">R<sub>2</sub></span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">10</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">0.1</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">400</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">400</span></div>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">R<sub>3</sub></span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">10</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">0.1</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">650</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; vertical-align:top; width:120px">
			<div style="text-align:center"><span style="font-size:28px">600</span></div>
			</td>
		</tr>
	</tbody>
</table>