<p style="text-align:justify"><span style="font-size:14px">Usually, power system reactance is much larger than its resistance. Therefore, we can write:</span></p>

<p style="text-align:justify"><span style="font-size:14px">Z<sub>1</sub> = X<sub>1</sub>, Z<sub>2</sub> = X<sub>2,</sub> Z<sub>0</sub> = X<sub>0</sub>. And assuming Z<sub>f</sub> = R<sub>f</sub> = 0,</span></p>

<p style="text-align:justify"><span style="font-size:14px">Magnitude of fault current for a three-phase fault,</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(I_{LLL}=\frac{E}{X_1} \)</span></span></p>

<p style="text-align:justify"><span style="font-size:14px">And that for a single line to ground fault</span></p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(I_{Lg}=\frac{3E}{X_1+X_2+X_0+3X_n}\)</span>&nbsp;</span></p>

<p style="text-align:justify"><span style="font-size:14px">We have introduced pure reactor in the neutral circuit, which is usually the case.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></p>

<p style="text-align:justify"><span style="font-size:14px">Now there are three possibilities:</span></p>

<ol>
	<li style="text-align:justify">
	<p><span style="font-size:14px">Solidly grounded or effectively grounded system: X<sub>n</sub> = 0, X<sub>1</sub> = X<sub>2</sub> for all static electrical equipment (i.e., transformers and transmission lines). If we assume X<sub>1</sub> = X<sub>2</sub> for generators also, which is not much far from reality. X<sub>0</sub> &lt;&lt; X<sub>1</sub> for generators. Substituting these conditions,</span></p>

	<p style="text-align:justify"><span style="font-size:14px">&nbsp;<span class="math-tex">\(I_{Lg}=\frac{3E}{2X_1}\)</span>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<span class="math-tex">\(I_{LLL}=\frac{E}{X_1}\)</span></span></p>

	<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(\dot{.\hspace{0.045in}.}\hspace{0.3cm}I_{Lg}&gt;I_{LLL}\)</span></span></p>

	<p style="text-align:justify"><span style="font-size:14px">This means that a single line to ground fault at the terminals of a generator with solidly grounded neutral is more severe than a three-phase fault at the same location.</span></p>
	</li>
	<li style="text-align:justify">
	<p style="text-align:justify"><span style="font-size:14px">Non-effective grounding of neutral of the generator:</span></p>

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

	<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(I_{Lg}=\frac{3E}{2X_1+3X_n}\)</span>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;I<sub>LLL</sub> does not change as it does not depend upon X<sub>n</sub>.</span></p>

	<p style="text-align:justify"><span style="font-size:14px">For I<sub>LLL</sub> and I<sub>Lg</sub> to be equal,</span></p>

	<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(\frac{3E}{2X_1+3X_n}=\frac{E}{X_1}\)</span></span></p>

	<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(\dot{.\hspace{0.045in}.}\hspace{0.3cm}X_n=\frac{X_1}{3}\)</span></span></p>
	</li>
</ol>

<p style="text-align:justify"><span style="font-size:14px">If <span class="math-tex">\(X_n&lt;\frac{X_1}{3}\)</span>, L-g fault is more severe than L-L-L-g fault and if <span class="math-tex">\(X_n&gt;\frac{X_1}{3}\)</span>, L-L-L-g fault is more severe than L-g fault. The probability of L-g fault is much more than that of L-L-L-g fault. Therefore, generators are usually grounded through very high impedance (reactance). The consequence of this high value of neutral reactance is high overvoltage as shown in figure 4.41. Neutral point (star point) is at zero potential under normal operating conditions. But when single line to ground fault (or double line to ground fault) occurs as shown in figure 4.41, neutral voltage is equal to I<sub>f</sub> X<sub>n</sub> w. r. t. ground. Therefore, voltage of R phase (Y phase and B phase also) w. r. t. ground,<img alt="" src="https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16162247391616224739.jpg" style="height:545px; width:800px" /></span></p>

<p style="text-align:justify"><span style="font-size:14px">V<sub>Rg</sub> = V<sub>ph-n</sub> + I<sub>f</sub> X<sub>n</sub>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(obviously, vectorially) </span></p>

<p style="text-align:justify"><span style="font-size:14px">Similarly, there will be overvoltage in Y and B phase also. If the neutral impedance is very large (Z<sub>n</sub> in case of 210 MW generators is of the order of 4000 ohms), the voltage of R, Y and B phases w. r. t. ground will be approximately line to line voltage of the generator. Therefore, line to line voltages V<sub>RY</sub>, V<sub>YB</sub> and V<sub>BR</sub> will be <span class="math-tex">\(\sqrt3\)</span>&nbsp;times normal line to line voltage of the generator.</span></p>

<p style="text-align:justify"><span style="font-size:14px">This means that the insulation of the generator windings and generator connections to the generator transformer (GT) has to be designed to withstand high voltage. This adds a lot to the cost of generator. But as GT is 10-20 meters away from the generator and hence the increased insulation level is only for generator, connecting leads (bus duct) up to GT and GT primary, the high impedance grounding is preferred. In case of generator, limiting the magnitude of earth-fault currents assumes priority. </span></p>

<p style="text-align:justify"><span style="font-size:14px">In general, we can conclude that all low voltage and medium voltage (6.6 kV, 11 kV) systems are non-effectively grounded. Whereas, all high voltage (66 kV, 132 kV), extra high voltage (220 kV, 400 kV) and ultra high voltage (765 kV and beyond) systems are solidly grounded. If we use non-effective grounding for such systems, the insulation cost of line insulators for line lengths ranging from 50 km to 500 km will be exorbitantly high. The fault current for earth-faults in the vicinity of transformers will be high in this case, but sensitive and fast-acting earth-fault protection can relieve the transformer from damages.</span></p>

<ol start="3">
	<li style="text-align:justify">
	<p style="text-align:justify"><span style="font-size:14px">For faults on transmission line away from source, as X<sub>0</sub> &gt;&gt;X<sub>1</sub>, I<sub>LLL</sub> &gt;&gt; I<sub>Lg</sub></span></p>
	</li>
</ol>

<p style="text-align:justify"><span style="font-size:14px">Therefore, the electrical equipments are relieved of high earth-fault currents (when earth-faults frequently occur) and damages due to that.</span></p>

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

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

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