<p style="text-align:justify"><img alt="" src="https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16253803861625380386.jpg" style="height:383px; width:800px" /></p>

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

<p style="text-align:justify"><span style="font-size:14px"><strong>Example 2:</strong> Figure 7.15 shows a single line diagram of a portion of a power system. Relays R<sub>1</sub>, R<sub>2</sub>&nbsp;And R<sub>3</sub> are standard IDMT overcurrent relays giving normal inverse characteristic. Each relay group is wired for three overcurrent and one earth-fault protection scheme. The setting range of ground overcurrent relays is 10-40 % of 1 amp in seven equal steps. The excitation current of all CTs is 0.05 amp. The minimum operating time for IDMT relays is constant beyond PSM = 20 and is 2.3 seconds at TMS = 1.0. The TMS of the relay R<sub>3</sub> is set at 0.2. The fault currents at different buses are as shown in table 7.5 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:66px; width:900px">
	<caption>
	<p><span style="font-size:18px"><strong>Table 7.5: Fault Currents at Different Buses</strong></span></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:102px">
			<div style="text-align:center"><strong><span style="font-size:28px">Fault at Bus</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:124px">
			<div style="text-align:center"><strong><span style="font-size:28px">Fault Current for L-L-L fault in 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:123px">
			<div style="text-align:center"><strong><span style="font-size:28px">Fault Current for L-L fault in 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:123px">
			<div style="text-align:center"><strong><span style="font-size:28px">Fault Current for L-g fault in 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:102px">
			<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; vertical-align:top; width:124px">
			<div style="text-align:center"><span style="font-size:28px">2100</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">1818</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">2714</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:102px">
			<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; vertical-align:top; width:124px">
			<div style="text-align:center"><span style="font-size:28px">1580</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">1366</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">1653</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:102px">
			<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:124px">
			<div style="text-align:center"><span style="font-size:28px">1264</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">1094</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">1192</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:102px">
			<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:124px">
			<div style="text-align:center"><span style="font-size:28px">1054</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">912</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">928</span></div>
			</td>
		</tr>
	</tbody>
</table>

<p>&nbsp;</p>

<p>&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">Determine the settings of ground relays R<sub>1</sub>, R<sub>2</sub> and R<sub>3</sub>.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><strong><u>Solution:</u></strong></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, assumed).</span></p>

<p style="text-align:justify"><span style="font-size:14px">Therefore, P. S. of R<sub>3</sub> = 0.1 amp.</span></p>

<p style="text-align:justify"><span style="font-size:14px">CT secondary current required to inject this current through the ground relay R<sub>3</sub> = 0.1 + 3(0.5)</span></p>

<p style="text-align:justify"><span style="font-size:14px">Therefore, CT secondary current at relaying point R<sub>3</sub> = 0.25 amp.</span></p>

<p style="text-align:justify"><span style="font-size:14px">CT primary equivalent of this current is 25 amp (CT ratio 100/1).</span></p>

<p style="text-align:justify"><span style="font-size:14px">Therefore, P. S. of the ground relay R<sub>3</sub> in CT primary terms is 25 amp.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(&gt; \frac{1.3}{1.05}\times\)</span>&nbsp;P. S. of relay R<sub>3</sub></span></p>

<p style="text-align:justify"><span style="font-size:14px"><sub><span class="math-tex">\(&gt;\frac{1.3}{1.05}\times25\)</span></sub></span></p>

<p style="text-align:justify"><span style="font-size:14px"><sub><span class="math-tex">\(&gt; 30.95 \)</span></sub>&nbsp;amp (CT primary)</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">This current reflected in CT secondary will be 0.103 amp (CT ratio at relaying point R<sub>2</sub> is 300/1). When excitation current (3 times 0.05) is deducted, the figure is negative. This means that minimum setting 10 % for relay R<sub>2</sub> will be certainly higher than 30.95 amp calculated above. Calculating in a different way, plug-setting 10 % mean 0.1 amp. Adding excitation current requirements of 3 CTs and transforming that secondary current to primary of 300/1 CT, the plug-setting is 75 amp which is more than 30.95 amp as required. Similarly, P. S. of R<sub>1</sub> is to be set at 10 %.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><strong><u>Time Settings:</u></strong></span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><strong><u>Coordination of R<sub>2</sub>-R<sub>3</sub></u>:</strong> I<sub>f</sub> = 1192 amp (Current for L-g fault at bus C).</span></p>

<p style="text-align:justify"><span style="font-size:14px">CT secondary equivalent, i<sub>f</sub> = 11.92 amp. Therefore, current through the ground relay R<sub>3</sub></span></p>

<p style="text-align:justify"><span style="font-size:14px">&nbsp;= 11.92 &ndash; 0.15 amp = 11.77 amp.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">PSM of ground relay R<sub>3</sub> </span></p>

<p style="text-align:justify"><span style="font-size:14px"><sub><span class="math-tex">\(=\frac{11.77}{0.1}\)</span></sub></span></p>

<p style="text-align:justify"><span style="font-size:14px"><sub>=117.7,</sub></span></p>

<p style="text-align:justify"><span style="font-size:14px"><sub><span class="math-tex">\(\dot{.\hspace{0.095in}.}\hspace{0.3cm}Top\hspace{0.2cm}of\hspace{0.2cm}R_3\)</span></sub>&nbsp;&nbsp;</span></p>

<p style="text-align:justify"><span style="font-size:14px">&nbsp; &nbsp; &nbsp;&nbsp;<span class="math-tex">\(=\frac{3}{log_{10}20}\times0.2\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">&nbsp; &nbsp; &nbsp; = 0.46 sec.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">Therefore, Top of R<sub>2</sub> = 0.71 sec. I<sub>f</sub> (1192 amp) seen in secondary of 300/1 CT = 3.973 amp.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px">Therefore, current through the ground relay R<sub>2</sub> = 3.82 amp.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(\dot{.\hspace{0.095in}.}\hspace{0.3cm}PSM\hspace{0.2cm}of\hspace{0.2cm}R_2\)</span>&nbsp;= 38.2.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(\frac{3}{log_{10}PSM\hspace{0.2cm}of\hspace{0.2cm}R_2}\times TMS\hspace{0.2cm}of\hspace{0.2cm}R_2\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">=0.71.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(\dot{.\hspace{0.095in}.}\hspace{0.3cm}TSM\hspace{0.1cm}of\hspace{0.1cm}R_2\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">&nbsp; &nbsp; &nbsp;&nbsp;<em>=0.308.</em>&nbsp;Hence, TMS = 0.35 selected.</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> = 1653 amp. Therefore, CT secondary equivalent (300/1 CT) i<sub>f</sub> = 5.51 amp.</span></p>

<p style="text-align:justify"><span style="font-size:14px">Current through the ground relay R<sub>2</sub> = 5.51 &ndash; 0.15 = 5.36 amp. </span></p>

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

<p style="text-align:justify"><span style="font-size:14px">PSM of R<sub>2&nbsp;</sub><span class="math-tex">\(=\frac{5.36}{0.1}\)</span>&nbsp;= 53.6.</span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><sub><span class="math-tex">\(=\frac{3}{log_{10}20}\times0.35\)</span></sub></span></p>

<p style="text-align:justify"><span style="font-size:14px"><sub>= 0.807 sec,</sub></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(\dot{.\hspace{0.095in}.}\hspace{0.3cm}Top\hspace{0.2cm}of\hspace{0.2cm}R_1\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">&nbsp; &nbsp; &nbsp; &nbsp;<em>=1.057 sec.</em></span></p>

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

<p style="text-align:justify"><span style="font-size:14px">I<sub>f</sub> seen in secondary of 750/1 CT = 2.204 amp. Hence, current through ground relay R<sub>1</sub>= 2.054 amp. PSM of R<sub>1</sub> = 20.54.</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(\dot{.\hspace{0.095in}.}\hspace{0.3cm}TSM\hspace{0.1cm}of\hspace{0.1cm}R_1\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">&nbsp; &nbsp; &nbsp;&nbsp;<span class="math-tex">\(=\frac{1.057\times log_{10}20}{3}\)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">&nbsp; &nbsp; &nbsp; = 0.458.</span></p>

<p style="text-align:justify"><span style="font-size:14px">Hence TMS of R<sub>1&nbsp;</sub>will be set at 0.5.</span></p>

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

<table cellspacing="0" class="MsoTableGrid" style="border-collapse:collapse; border:none; margin-left:94px; width:900px">
	<caption>
	<p><strong><span style="font-size:18px">Table 7.6: Summary of Settings of Relays of Example 2</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:106px">
			<div style="text-align:center"><span style="font-size:28px">Ground Relay</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:111px">
			<div style="text-align:center"><span style="font-size:28px">P.S. as % of Relay Rating</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:104px">
			<div style="text-align:center"><span style="font-size:28px">TMS</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:106px">
			<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:111px">
			<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:104px">
			<div style="text-align:center"><span style="font-size:28px">0.2</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:106px">
			<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:111px">
			<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:104px">
			<div style="text-align:center"><span style="font-size:28px">0.35</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:106px">
			<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:111px">
			<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:104px">
			<div style="text-align:center"><span style="font-size:28px">0.5</span></div>
			</td>
		</tr>
	</tbody>
</table>

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

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

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

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

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