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		<title>Two Reaction Theory – Salient Pole Synchronous Machine</title>
		<link>https://circuitglobe.com/two-reaction-theory-salient-pole-synchronous-machine.html</link>
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		<dc:creator><![CDATA[bhakti]]></dc:creator>
		<pubDate>Wed, 20 Jan 2016 11:19:13 +0000</pubDate>
				<category><![CDATA[Synchronous Machines]]></category>
		<guid isPermaLink="false">https://circuitglobe.com/?p=2851</guid>

					<description><![CDATA[<p>Two Reaction Theory was proposed by Andre Blondel. The theory proposes to resolve the given armature MMFs into two mutually perpendicular components, with one located along the axis of the rotor of the salient pole. It is known as the direct axis or d axis component. The other component is located perpendicular to the axis &#8230;</p>
<p class="read-more"> <a class="" href="https://circuitglobe.com/two-reaction-theory-salient-pole-synchronous-machine.html"> <span class="screen-reader-text">Two Reaction Theory – Salient Pole Synchronous Machine</span> Read More »</a></p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/two-reaction-theory-salient-pole-synchronous-machine.html">Two Reaction Theory – Salient Pole Synchronous Machine</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p><strong>Two Reaction Theory</strong> was proposed by<strong> Andre Blondel</strong>. The theory proposes to resolve the given armature MMFs into two mutually perpendicular components, with one located along the axis of the rotor of the salient pole. It is known as the <strong>direct axis</strong> or <strong>d axis</strong> component. The other component is located perpendicular to the axis of the rotor salient pole. It is known as the <strong>quadrature axis</strong> or<strong> q axis</strong> component.</p>
<p>The d axis component of the armature MMF, F<sub>a </sub>is denoted by F<sub>d, </sub>and the q axis component by F<sub>q</sub>. The component F<sub>d</sub> is either magnetizing or demagnetizing. The component F<sub>q </sub>results in a cross-magnetizing effect. If Ψ is the angle between the armature current I<sub>a</sub> and the excitation voltage E<sub>f </sub>and F<sub>a</sub> is the amplitude of the armature MMF, then<a href="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-1-compressor.jpg" rel="attachment wp-att-2852"><img decoding="async" loading="lazy" class="size-full wp-image-2852 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-1-compressor.jpg" alt="TWO-REACTION-THEORY-EQ-1" width="247" height="89" /></a></p>
<h2>Salient Pole Synchronous Machine Two Rection Theory</h2>
<p>In the cylindrical rotor synchronous machine, the air gap is uniform. The pole structure of the rotor of a salient pole machine makes the air gap highly non-uniform. Consider a 2 pole, salient pole rotor rotating in the anticlockwise direction within a 2 pole stator as shown in the figure below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/two-reaction-theory-fig-1.jpg" rel="attachment wp-att-3358"><img decoding="async" loading="lazy" class="aligncenter wp-image-3358" src="https://circuitglobe.com/wp-content/uploads/2016/01/two-reaction-theory-fig-1.jpg" alt="two-reaction-theory-fig-1" width="417" height="304" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/two-reaction-theory-fig-1.jpg 472w, https://circuitglobe.com/wp-content/uploads/2016/01/two-reaction-theory-fig-1-300x219.jpg 300w" sizes="(max-width: 417px) 100vw, 417px" /></a>The axis along the axis of the rotor is called the direct or the d axis. The axis perpendicular to the d axis is known as the quadrature or q axis. The direct axis flux path involves two small air gaps and is the path of the minimum reluctance. The path shown in the above figure by ϕ<sub>q</sub> has two large air gaps and is the path of the maximum reluctance.</p>
<p>The rotor flux B<sub>R</sub> is shown vertically upwards as shown in the figure below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/two-reaction-theory-fig-2.jpg" rel="attachment wp-att-3359"><img decoding="async" loading="lazy" class="aligncenter wp-image-3359" src="https://circuitglobe.com/wp-content/uploads/2016/01/two-reaction-theory-fig-2.jpg" alt="Two reaction theory of salient pole fig 2" width="476" height="249" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/two-reaction-theory-fig-2.jpg 676w, https://circuitglobe.com/wp-content/uploads/2016/01/two-reaction-theory-fig-2-300x157.jpg 300w" sizes="(max-width: 476px) 100vw, 476px" /></a>The rotor flux induces a voltage E<sub>f</sub> in the stator. The stator armature current I<sub>a</sub> will flow through the synchronous motor when a lagging power factor load is connected to it. This stator armature current I<sub>a</sub> lags behind the generated voltage E<sub>f </sub>by an angle Ψ.</p>
<p>The armature current produces stator magnetomotive force F<sub>s</sub>. This MMF lags behind I<sub>a</sub> by angle 90 degrees. The MMF F<sub>S</sub> produces stator magnetic field B<sub>S</sub> long the direction of Fs. The stator MMF is resolved into two components, namely the direct axis component F<sub>d</sub> and the quadrature axis component F<sub>q</sub>.</p>
<p>If,</p>
<ul>
<li>ϕ<sub>d </sub>is the direct axis flux</li>
<li>Φ<sub>q</sub> is the quadrature axis flux</li>
<li>R<sub>d</sub> is the reluctance of the direct axis flux path</li>
</ul>
<p>Therefore<a href="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-2-compressor.jpg" rel="attachment wp-att-2855"><img decoding="async" loading="lazy" class="size-full wp-image-2855 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-2-compressor.jpg" alt="TWO-REACTION-THEORY-EQ-2" width="130" height="152" /></a></p>
<p>As, R<sub>d</sub> &lt; R<sub>q</sub>, the direct axis component of MMF F<sub>d</sub> produces more flux than the quadrature axis component of the MMF. The fluxes of the direct and quadrature axis produce a voltage in the windings of the stator by armature reaction.</p>
<p>Let,</p>
<ul>
<li>E<sub>ad</sub> be the direct axis component of the armature reaction voltage.</li>
<li>E<sub>aq </sub>be the quadrature axis component of the armature reaction voltage.</li>
</ul>
<p>Since each armature reaction voltage is directly proportional to its stator current and lags behind by 90 degrees angles. Therefore, armature reaction voltages can be written as shown below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-3-compressor.jpg" rel="attachment wp-att-2856"><img decoding="async" loading="lazy" class="size-full wp-image-2856 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-3-compressor.jpg" alt="TWO-REACTION-THEORY-EQ-3" width="279" height="104" /></a></p>
<p>Where,</p>
<ul>
<li>X<sub>ad</sub> is the armature reaction reactance in the direct axis per phase.</li>
<li>X<sub>aq</sub> is the armature reaction reactance in the quadrature axis per phase.</li>
</ul>
<p>The value of X<sub>ad</sub> is always greater than X<sub>aq</sub>. As the EMF induced by a given MMF acting on the direct axis is smaller than for the quadrature axis due to its higher reluctance.</p>
<p>The total voltage induced in the stator is the sum of EMF induced by the field excitation. The equations are written as follows:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-4-compressor.jpg" rel="attachment wp-att-2857"><img decoding="async" loading="lazy" class="size-full wp-image-2857 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-4-compressor.jpg" alt="TWO-REACTION-THEORY-EQ-4" width="375" height="103" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-4-compressor.jpg 375w, https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-4-compressor-300x82.jpg 300w" sizes="(max-width: 375px) 100vw, 375px" /></a></p>
<p>The voltage E’ is equal to the sum of the terminal voltage V and the voltage drops in the resistance and leakage reactance of the armature. The equation is written as:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-5-compressor.jpg" rel="attachment wp-att-2858"><img decoding="async" loading="lazy" class="size-full wp-image-2858 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-5-compressor.jpg" alt="TWO-REACTION-THEORY-EQ-5" width="341" height="60" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-5-compressor.jpg 341w, https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-5-compressor-300x53.jpg 300w" sizes="(max-width: 341px) 100vw, 341px" /></a></p>
<p>The armature current is divided into two components; one is the phase with the excitation voltage E<sub>f </sub>and the other is in phase quadrature to it.</p>
<p>If</p>
<ul>
<li>I<sub>q</sub> is the axis component of I<sub>a</sub> in phase with E<sub>f</sub>.</li>
<li>I<sub>d</sub> is the d axis I<sub>a</sub> lagging E<sub>f</sub> by 90 degrees.</li>
</ul>
<p>Therefore,<a href="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-6-compressor.jpg" rel="attachment wp-att-2859"><img decoding="async" loading="lazy" class="size-full wp-image-2859 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-6-compressor.jpg" alt="TWO-REACTION-THEORY-EQ-6" width="233" height="46" /></a></p>
<p>Combining the equation (4) and (5) we get,<a href="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-7-compressor.jpg" rel="attachment wp-att-2860"><img decoding="async" loading="lazy" class="size-full wp-image-2860 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-7-compressor.jpg" alt="TWO-REACTION-THEORY-EQ-7" width="493" height="55" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-7-compressor.jpg 493w, https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-7-compressor-300x33.jpg 300w" sizes="(max-width: 493px) 100vw, 493px" /></a></p>
<p>Combining the equation (6) and (7) we get,<a href="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-8-compressor.jpg" rel="attachment wp-att-2861"><img decoding="async" loading="lazy" class="size-full wp-image-2861 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-8-compressor.jpg" alt="TWO-REACTION-THEORY-EQ-8" width="663" height="103" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-8-compressor.jpg 663w, https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-8-compressor-300x47.jpg 300w" sizes="(max-width: 663px) 100vw, 663px" /></a> Let,<a href="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-9.png" rel="attachment wp-att-2862"><img decoding="async" loading="lazy" class="size-full wp-image-2862 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-9.png" alt="TWO REACTION THEORY EQ 9" width="268" height="96" /></a></p>
<p>The reactance <strong>X<sub>d</sub></strong> is called the <strong>direct axis synchronous reactance</strong>, and the reactance<strong> X</strong><sub><strong>q</strong> </sub>is called the<strong> quadrature axis synchronous reactance.</strong></p>
<p>Combining the equations (9) (10) and (11), we get the equations shown below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-10-compressor.jpg" rel="attachment wp-att-2863"><img decoding="async" loading="lazy" class="size-full wp-image-2863 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-10-compressor.jpg" alt="TWO-REACTION-THEORY-EQ-10" width="537" height="101" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-10-compressor.jpg 537w, https://circuitglobe.com/wp-content/uploads/2016/01/TWO-REACTION-THEORY-EQ-10-compressor-300x56.jpg 300w" sizes="(max-width: 537px) 100vw, 537px" /></a> The equation (12) shown above is the final voltage equation for a salient pole synchronous generator.</p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/two-reaction-theory-salient-pole-synchronous-machine.html">Two Reaction Theory – Salient Pole Synchronous Machine</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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		<title>Armature Reaction in a Synchronous Machine</title>
		<link>https://circuitglobe.com/armature-reaction-in-synchronous-machine.html</link>
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		<dc:creator><![CDATA[bhakti]]></dc:creator>
		<pubDate>Tue, 19 Jan 2016 09:28:02 +0000</pubDate>
				<category><![CDATA[Synchronous Machines]]></category>
		<guid isPermaLink="false">https://circuitglobe.com/?p=2734</guid>

					<description><![CDATA[<p>The effect of Armature (stator) flux on the flux produced by the rotor field poles is called Armature Reaction. When the current flows through the armature winding of the alternator, a flux is produced by the resulting MMF. This armature flux reacts with the main pole flux, causing the resultant flux to become either less &#8230;</p>
<p class="read-more"> <a class="" href="https://circuitglobe.com/armature-reaction-in-synchronous-machine.html"> <span class="screen-reader-text">Armature Reaction in a Synchronous Machine</span> Read More »</a></p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/armature-reaction-in-synchronous-machine.html">Armature Reaction in a Synchronous Machine</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
]]></description>
										<content:encoded><![CDATA[<p>The effect of Armature (stator) flux on the flux produced by the rotor field poles is called <strong>Armature Reaction</strong>. When the current flows through the armature winding of the alternator, a flux is produced by the resulting MMF. This armature flux reacts with the main pole flux, causing the resultant flux to become either less than or more than the original main field flux.</p>
<p>For simplicity, we consider a <strong>3 phase, 2 pole alternator</strong> shown in the figure below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-1-compressor.jpg" rel="attachment wp-att-2735"><img decoding="async" loading="lazy" class="aligncenter wp-image-2735" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-1-compressor.jpg" alt="ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-1" width="363" height="361" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-1-compressor.jpg 439w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-1-compressor-150x150.jpg 150w" sizes="(max-width: 363px) 100vw, 363px" /></a></p>
<p>The winding of each pole is assumed to be concentrated, but the effects of armature reaction will be the same as if a distributed winding were also used. The armature reaction in a synchronous machine affects the main field flux and varies differently for different power factors.</p>
<p>Here armature reaction is discussed for the following three conditions, namely unity power factor, zero power factor lagging, and zero power factor leading. The <strong>power factor</strong> can be defined as the cosine of the angle between the armature phase current and the induced EMF in the armature conductor in that phase.</p>
<h2>Armature Reaction at Unity Power Factor</h2>
<p>The direction of rotation of the rotor is considered clockwise. By applying the right-hand rule, the direction of the induced emf in various conductors can be found. The direction of rotation of the conductors is taken anticlockwise with respect to the rotor poles.</p>
<p>Suppose that the alternator is supplying current at unity power factor. The phase currents I<sub>A</sub>, I<sub>B</sub>, and I<sub>C</sub> will be in phase with their respective generated voltages, i.e., E<sub>A</sub>, E<sub>B</sub>, and E<sub>C</sub> as shown in the figure below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-2-compressor.jpg" rel="attachment wp-att-2736"><img decoding="async" loading="lazy" class="aligncenter wp-image-2736" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-2-compressor.jpg" alt="ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-2" width="344" height="388" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-2-compressor.jpg 463w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-2-compressor-266x300.jpg 266w" sizes="(max-width: 344px) 100vw, 344px" /></a></p>
<p>The positive direction of fluxes ϕ<sub>A</sub>, ϕ<sub>B</sub>, ϕ<sub>C</sub> are shown in the figure below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-3-compressor.jpg" rel="attachment wp-att-2737"><img decoding="async" loading="lazy" class="aligncenter wp-image-2737" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-3-compressor.jpg" alt="ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-3" width="421" height="369" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-3-compressor.jpg 551w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-3-compressor-300x263.jpg 300w" sizes="(max-width: 421px) 100vw, 421px" /></a>The projection of a phasor on the vertical axis gives its instantaneous value.</p>
<p>At<strong> t=0</strong>, the instantaneous values of currents and fluxes are given by the equation shown below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-1-compressor.jpg" rel="attachment wp-att-2738"><img decoding="async" loading="lazy" class="size-full wp-image-2738 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-1-compressor.jpg" alt="ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-1" width="502" height="183" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-1-compressor.jpg 502w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-1-compressor-300x109.jpg 300w" sizes="(max-width: 502px) 100vw, 502px" /></a></p>
<p>Where the subscript m denotes the maximum values of current and flux. Thus, the flux ϕ<sub>A</sub> is along with OA, and the fluxes ϕ<sub>B</sub> and ϕ<sub>C</sub> are negative and acts opposite to each other represented by OB and OC respectively as shown in the figure below. The resultant of the fluxes can be found by resolving the fluxes horizontally and vertically.</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-4-compressor.jpg" rel="attachment wp-att-2739"><img decoding="async" loading="lazy" class="aligncenter wp-image-2739" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-4-compressor.jpg" alt="ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-4" width="473" height="309" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-4-compressor.jpg 713w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-4-compressor-300x196.jpg 300w" sizes="(max-width: 473px) 100vw, 473px" /></a>Resolving along the horizontal direction we get<a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-2-compressor.jpg" rel="attachment wp-att-2740"><img decoding="async" loading="lazy" class="size-full wp-image-2740 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-2-compressor.jpg" alt="ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-2" width="435" height="180" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-2-compressor.jpg 435w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-2-compressor-300x124.jpg 300w" sizes="(max-width: 435px) 100vw, 435px" /></a></p>
<p>Similarly, resolving along the vertical direction we get<a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-3-compressor.jpg" rel="attachment wp-att-2741"><img decoding="async" loading="lazy" class="size-full wp-image-2741 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-3-compressor.jpg" alt="ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-3" width="405" height="114" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-3-compressor.jpg 405w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-3-compressor-300x84.jpg 300w" sizes="(max-width: 405px) 100vw, 405px" /></a></p>
<p>The resultant armature reaction flux is given by<a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-4-compressor.jpg" rel="attachment wp-att-2742"><img decoding="async" loading="lazy" class="size-full wp-image-2742 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-4-compressor.jpg" alt="ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-4" width="396" height="126" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-4-compressor.jpg 396w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-4-compressor-300x95.jpg 300w" sizes="(max-width: 396px) 100vw, 396px" /></a></p>
<p>If the rotor is rotated, 30 degrees in a clockwise direction, the corresponding phasor diagram is shown below.</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-5-compressor.jpg" rel="attachment wp-att-2744"><img decoding="async" loading="lazy" class="aligncenter wp-image-2744 size-medium" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-5-compressor-287x300.jpg" alt="ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-5" width="287" height="300" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-5-compressor-287x300.jpg 287w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-5-compressor.jpg 436w" sizes="(max-width: 287px) 100vw, 287px" /></a></p>
<p>At the instant when <strong>ωt = 30⁰</strong>, the instantaneous values of currents and fluxes are given as:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-5-compressor.jpg" rel="attachment wp-att-2745"><img decoding="async" loading="lazy" class="size-full wp-image-2745 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-5-compressor.jpg" alt="ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-5" width="521" height="201" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-5-compressor.jpg 521w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-5-compressor-300x116.jpg 300w" sizes="(max-width: 521px) 100vw, 521px" /></a></p>
<p>The space diagram for fluxes at ωt = 30⁰ is shown below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-6-compressor.jpg" rel="attachment wp-att-2743"><img decoding="async" loading="lazy" class="aligncenter wp-image-2743" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-6-compressor.jpg" alt="ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-6" width="437" height="300" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-6-compressor.jpg 537w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-6-compressor-300x206.jpg 300w" sizes="(max-width: 437px) 100vw, 437px" /></a></p>
<p>Here, <strong>ϕ<sub>B</sub> = 0</strong>. The resultant armature reaction flux is given by the equation shown below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-6-compressor.jpg" rel="attachment wp-att-2746"><img decoding="async" loading="lazy" class="size-full wp-image-2746 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-6-compressor.jpg" alt="ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-6" width="476" height="127" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-6-compressor.jpg 476w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-6-compressor-300x80.jpg 300w" sizes="(max-width: 476px) 100vw, 476px" /></a></p>
<p>The direction of the resultant flux ϕ<sub>AR</sub> is along OD, which makes an angle with the horizontal in the clockwise direction.</p>
<p>Hence, it is observed that the resultant flux ϕ<sub>AR</sub> sets up by the current in the armature remains constant in magnitude equal to 1.5 ϕ<sub>m </sub>and it rotates at synchronous speed. When the current is in phase with the induced voltage the armature reaction flux ϕ<sub>AR</sub> lags behind the main field by 90⁰. This is called <strong>Cross Magnetizing Flux.</strong></p>
<h2>Armature Reaction at Lagging Power Factor</h2>
<p>If the alternator is loaded with an inductive load of zero power factor lagging. The phase current I<sub>A</sub>, I<sub>B</sub> and I<sub>C</sub> will be lagging with their respective phase voltages E<sub>A</sub>, E<sub>B</sub> and E<sub>C</sub> by 90⁰. The figure below shows the phasor diagram of armature reaction at lagging load.</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-7-compressor.jpg" rel="attachment wp-att-2747"><img decoding="async" loading="lazy" class="aligncenter wp-image-2747" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-7-compressor.jpg" alt="ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-7" width="413" height="378" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-7-compressor.jpg 513w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-7-compressor-300x274.jpg 300w" sizes="(max-width: 413px) 100vw, 413px" /></a></p>
<p>At time<strong> t = 0</strong>, the instantaneous values of currents and fluxes are given by:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-7-compressor.jpg" rel="attachment wp-att-2748"><img decoding="async" loading="lazy" class="size-full wp-image-2748 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-7-compressor.jpg" alt="ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-7" width="530" height="206" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-7-compressor.jpg 530w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-7-compressor-300x117.jpg 300w" sizes="(max-width: 530px) 100vw, 530px" /></a></p>
<p>The<strong> space diagram</strong> of the magnetic fluxes is shown below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-8-compressor.jpg" rel="attachment wp-att-2749"><img decoding="async" loading="lazy" class="aligncenter wp-image-2749" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-8-compressor.jpg" alt="ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-8" width="418" height="286" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-8-compressor.jpg 621w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-8-compressor-300x205.jpg 300w" sizes="(max-width: 418px) 100vw, 418px" /></a></p>
<p>The resultant flux ϕ<sub>AR</sub> is given by the equation shown below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-8-compressor.jpg" rel="attachment wp-att-2750"><img decoding="async" loading="lazy" class="size-full wp-image-2750 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-8-compressor.jpg" alt="ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-8" width="619" height="181" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-8-compressor.jpg 619w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-8-compressor-300x88.jpg 300w" sizes="(max-width: 619px) 100vw, 619px" /></a></p>
<p>The direction of the armature reaction flux is opposite to the main field flux. Therefore, it will oppose and weaken the main field flux. It is said to be demagnetized.</p>
<h2>Armature Reaction at Leading Power Factor</h2>
<p>If the alternator is loaded with a load of zero power factor leading. The phase currents I<sub>A</sub>, I<sub>B,</sub> and I<sub>C</sub> will be leading their respective phase voltages E<sub>A</sub>, E<sub>B,</sub> and E<sub>C</sub> by 90⁰. The phasor diagram is shown below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-9-compressor.jpg" rel="attachment wp-att-2751"><img decoding="async" loading="lazy" class="aligncenter wp-image-2751" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-9-compressor.jpg" alt="ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-9" width="378" height="355" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-9-compressor.jpg 514w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-9-compressor-300x282.jpg 300w" sizes="(max-width: 378px) 100vw, 378px" /></a></p>
<p>At time t = 0, the instantaneous values of currents and fluxes are given by the equations shown below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-9-compressor.jpg" rel="attachment wp-att-2752"><img decoding="async" loading="lazy" class="size-full wp-image-2752 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-9-compressor.jpg" alt="ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-9" width="524" height="200" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-9-compressor.jpg 524w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-9-compressor-300x115.jpg 300w" sizes="(max-width: 524px) 100vw, 524px" /></a></p>
<p>The direction of the flux is shown below in the phasor diagram.</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-10-compressor.jpg" rel="attachment wp-att-2753"><img decoding="async" loading="lazy" class="aligncenter wp-image-2753" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-10-compressor.jpg" alt="ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-10" width="492" height="379" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-10-compressor.jpg 592w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-OF-A-SYNCHRONOUS-MACHINE-FIG-10-compressor-300x231.jpg 300w" sizes="(max-width: 492px) 100vw, 492px" /></a></p>
<p>The resultant flux is given by the equation shown below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-10-compressor.jpg" rel="attachment wp-att-2754"><img decoding="async" loading="lazy" class="size-full wp-image-2754 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-10-compressor.jpg" alt="ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-10" width="622" height="184" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-10-compressor.jpg 622w, https://circuitglobe.com/wp-content/uploads/2016/01/ARMATURE-REACTION-IN-SYNCHRONOUS-MACHINE-EQ-10-compressor-300x89.jpg 300w" sizes="(max-width: 622px) 100vw, 622px" /></a> The direction of the armature reaction flux is in the direction of the main field flux. It is known as <strong>magnetizing flux.</strong></p>
<h3>Armature Reaction Nature</h3>
<p>The following conclusion is given below:</p>
<ul>
<li>The armature reaction flux is constant in magnitude and rotates at synchronous speed.</li>
<li>The armature reaction is cross-magnetizing when the generator supplies a load at unity power factor.</li>
<li>When the generator supplies a load, at lagging power, the armature reaction is partly demagnetizing and partly cross-magnetizing.</li>
</ul>
<p>This is all about Armature Reaction in a Synchronous Machine.</p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/armature-reaction-in-synchronous-machine.html">Armature Reaction in a Synchronous Machine</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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		<title>Effect of Load on a Synchronous Motor</title>
		<link>https://circuitglobe.com/effect-of-load-on-synchronous-motor.html</link>
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		<dc:creator><![CDATA[bhakti]]></dc:creator>
		<pubDate>Sat, 16 Jan 2016 11:23:57 +0000</pubDate>
				<category><![CDATA[Synchronous Machines]]></category>
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					<description><![CDATA[<p>A synchronous motor runs at constant synchronous speed, regardless of the load. Let us see the effect of the load change on the motor. Consider a synchronous motor operating initially with a leading power factor.  The phasor diagram for the leading power factor is shown below: The load on the shaft is increased. The rotor &#8230;</p>
<p class="read-more"> <a class="" href="https://circuitglobe.com/effect-of-load-on-synchronous-motor.html"> <span class="screen-reader-text">Effect of Load on a Synchronous Motor</span> Read More »</a></p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/effect-of-load-on-synchronous-motor.html">Effect of Load on a Synchronous Motor</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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										<content:encoded><![CDATA[<p>A <strong>synchronous motor</strong> runs at <strong>constant</strong> synchronous speed, regardless of the <strong>load</strong>. Let us see the effect of the load change on the motor. Consider a synchronous motor operating initially with a leading power factor.  The <strong>phasor diagram</strong> for the leading power factor is shown below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-Synchronous-Motor-FIG-1-compressor.jpg" rel="attachment wp-att-2727"><img decoding="async" loading="lazy" class="aligncenter wp-image-2727" src="https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-Synchronous-Motor-FIG-1-compressor.jpg" alt="Effect-of-load-on-Synchronous-Motor-FIG-1" width="310" height="326" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-Synchronous-Motor-FIG-1-compressor.jpg 504w, https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-Synchronous-Motor-FIG-1-compressor-285x300.jpg 285w" sizes="(max-width: 310px) 100vw, 310px" /></a></p>
<p>The load on the shaft is increased. The rotor slows down momentarily, as it required some time to take increased power from the line. In another word, it can be said that even if the rotor is rotating at synchronous speed, the rotor slips back in space because of the increase in the load. In this process, the torque angle δ becomes larger, and, as a result, the induced torque increases.</p>
<p>The induced torque equation is given as:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-synchronous-motor-eq-1-compressor.jpg" rel="attachment wp-att-2728"><img decoding="async" loading="lazy" class="size-full wp-image-2728 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-synchronous-motor-eq-1-compressor.jpg" alt="Effect-of-load-on-synchronous-motor-eq-1" width="186" height="69" /></a></p>
<p>Then increased torque increases the rotor speed, and the motor again regains the synchronous speed, but with the larger torque angle. The excitation voltage E<sub>f</sub> is proportional to ϕω, it depends upon the field current and the speed of the motor. Since the motor is moving at a synchronous speed, and the field current is also constant. Hence, the magnitude of the Voltage<strong> |E<sub>f</sub>|</strong> remains constant. We have,<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-synchronous-motor-eq-2-compressor.jpg" rel="attachment wp-att-2729"><img decoding="async" loading="lazy" class="size-full wp-image-2729 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-synchronous-motor-eq-2-compressor.jpg" alt="Effect-of-load-on-synchronous-motor-eq-2" width="517" height="196" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-synchronous-motor-eq-2-compressor.jpg 517w, https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-synchronous-motor-eq-2-compressor-300x114.jpg 300w" sizes="(max-width: 517px) 100vw, 517px" /></a></p>
<p>From the above equations, it is clear, that if P is increased the value of E<sub>f</sub> sinδ and I<sub>a</sub> cosϕ also increases.</p>
<p>The figure below shows the effect of an increase in load on the operation of a synchronous motor.</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-Synchronous-Motor-FIG-2-compressor.jpg" rel="attachment wp-att-2730"><img decoding="async" loading="lazy" class="aligncenter wp-image-2730" src="https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-Synchronous-Motor-FIG-2-compressor.jpg" alt="Effect-of-load-on-Synchronous-Motor-FIG-2" width="547" height="428" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-Synchronous-Motor-FIG-2-compressor.jpg 847w, https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-Synchronous-Motor-FIG-2-compressor-300x235.jpg 300w, https://circuitglobe.com/wp-content/uploads/2016/01/Effect-of-load-on-Synchronous-Motor-FIG-2-compressor-768x601.jpg 768w" sizes="(max-width: 547px) 100vw, 547px" /></a></p>
<p>It is seen from the above figure that with the increase in load, the quantity jI<sub>a</sub>X<sub>s</sub> goes on increasing and the relation<strong> V = E<sub>f</sub> + jI<sub>a</sub>X<sub>s</sub> is satisfied</strong>. The armature current is also increased. The power factor angle also changes with the change in load. It becomes less and less leading and then becomes more and more lagging as shown in the figure above.</p>
<p>Thus, if the load on a synchronous motor is increased the following points are considered which are given below.</p>
<ul>
<li>The motor continues to run at synchronous speed.</li>
<li>The torque angle δ increases.</li>
<li>The excitation voltage E<sub>f </sub>remains constant.</li>
<li>The armature current I<sub>a</sub> drawn from the supply increases.</li>
<li>The phase angle ϕ increases in the lagging direction.</li>
</ul>
<p>There is a limit to the mechanical load that can be applied to a synchronous motor. As the load is increased, the torque angle δ also increases until the condition arises when the rotor is<strong> pulled out of synchronism</strong> and the motor is stopped.</p>
<p><strong>Pull-out torque</strong> is defined as the maximum value of the torque which a synchronous motor can develop at rated voltage and frequency without losing synchronism. Its values vary from <strong>1.5</strong> to <strong>3.5</strong> times the full load torque.</p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/effect-of-load-on-synchronous-motor.html">Effect of Load on a Synchronous Motor</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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		<title>Short Circuit Ratio of a Synchronous Machine</title>
		<link>https://circuitglobe.com/short-circuit-ratio-of-a-synchronous-machine.html</link>
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		<dc:creator><![CDATA[bhakti]]></dc:creator>
		<pubDate>Sat, 16 Jan 2016 10:34:36 +0000</pubDate>
				<category><![CDATA[Synchronous Machines]]></category>
		<guid isPermaLink="false">https://circuitglobe.com/?p=2710</guid>

					<description><![CDATA[<p>The Short Circuit Ratio (SCR) of a synchronous machine is defined as the ratio of the field current required to generate rated voltage on an open circuit to the field current required to circulate rated armature current on a short circuit. The short circuit ratio can be calculated from the open-circuit characteristic ( O.C.C) at &#8230;</p>
<p class="read-more"> <a class="" href="https://circuitglobe.com/short-circuit-ratio-of-a-synchronous-machine.html"> <span class="screen-reader-text">Short Circuit Ratio of a Synchronous Machine</span> Read More »</a></p>
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]]></description>
										<content:encoded><![CDATA[<p>The<strong> Short Circuit Ratio (SCR)</strong> of a synchronous machine is defined as the ratio of the field current required to generate rated voltage on an open circuit to the field current required to circulate rated armature current on a short circuit. The short circuit ratio can be calculated from the <strong>open-circuit characteristic</strong> <strong>( O.C.C)</strong> at rated speed and the <strong>short circuit characteristic</strong> <strong>(S.C.C)</strong> of a three-phase synchronous machine as shown in the figure below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/ssc-graph.jpg"><img decoding="async" loading="lazy" class="aligncenter size-full wp-image-11380" src="https://circuitglobe.com/wp-content/uploads/2016/01/ssc-graph.jpg" alt="short-circuit-ratio-of-synchronous-motor" width="450" height="486" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/ssc-graph.jpg 450w, https://circuitglobe.com/wp-content/uploads/2016/01/ssc-graph-278x300.jpg 278w" sizes="(max-width: 450px) 100vw, 450px" /></a></p>
<p>From the above figure, the short circuit ratio is given by the equation shown below.<a href="https://circuitglobe.com/wp-content/uploads/2016/01/short-circuit-ratio-of-synchronous-machine-eq-1-compressor.jpg" rel="attachment wp-att-2712"><img decoding="async" loading="lazy" class="size-full wp-image-2712 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/short-circuit-ratio-of-synchronous-machine-eq-1-compressor.jpg" alt="short-circuit-ratio-of-synchronous-machine-eq-1" width="481" height="71" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/short-circuit-ratio-of-synchronous-machine-eq-1-compressor.jpg 481w, https://circuitglobe.com/wp-content/uploads/2016/01/short-circuit-ratio-of-synchronous-machine-eq-1-compressor-300x44.jpg 300w" sizes="(max-width: 481px) 100vw, 481px" /></a></p>
<p>Since the triangles Oab and Ode are similar. Therefore,<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-2-compressor-1.jpg"><img decoding="async" loading="lazy" class="aligncenter size-full wp-image-11378" src="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-2-compressor-1.jpg" alt="Short-Circuit-Ratio-of-Synchronous-Machine-eq-2-compressor" width="277" height="77" /></a></p>
<p>The direct axis synchronous reactance X<sub>d </sub>is defined as the ratio of open-circuit voltage for a given field current to the armature short circuit current for the same field current.</p>
<p>For the field current equal to Oa, the direct axis synchronous reactance in ohms is given by the equation shown below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-3-compressor.jpg" rel="attachment wp-att-2714"><img decoding="async" loading="lazy" class="size-full wp-image-2714 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-3-compressor.jpg" alt="Short-Circuit-Ratio-of-Synchronous-Machine-eq-3" width="214" height="61" /></a></p>
<p>The per-unit value of X<sub>d </sub>is given as:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-4-compressor.jpg" rel="attachment wp-att-2715"><img decoding="async" loading="lazy" class="size-full wp-image-2715 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-4-compressor.jpg" alt="Short-Circuit-Ratio-of-Synchronous-Machine-eq-4" width="352" height="66" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-4-compressor.jpg 352w, https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-4-compressor-300x56.jpg 300w" sizes="(max-width: 352px) 100vw, 352px" /></a></p>
<p>But, the base impedance is:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-5-compressor.jpg" rel="attachment wp-att-2716"><img decoding="async" loading="lazy" class="size-full wp-image-2716 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-5-compressor.jpg" alt="Short-Circuit-Ratio-of-Synchronous-Machine-eq-5" width="545" height="154" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-5-compressor.jpg 545w, https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-5-compressor-300x85.jpg 300w" sizes="(max-width: 545px) 100vw, 545px" /></a> Therefore,<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-6-compressor.jpg" rel="attachment wp-att-2717"><img decoding="async" loading="lazy" class="size-full wp-image-2717 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-6-compressor.jpg" alt="Short-Circuit-Ratio-of-Synchronous-Machine-eq-6" width="350" height="78" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-6-compressor.jpg 350w, https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-6-compressor-300x67.jpg 300w" sizes="(max-width: 350px) 100vw, 350px" /></a></p>
<p>From equation (1) and equation (6), we get<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-7-compressor.jpg" rel="attachment wp-att-2718"><img decoding="async" loading="lazy" class="size-full wp-image-2718 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-7-compressor.jpg" alt="Short-Circuit-Ratio-of-Synchronous-Machine-eq-7" width="428" height="79" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-7-compressor.jpg 428w, https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-7-compressor-300x55.jpg 300w" sizes="(max-width: 428px) 100vw, 428px" /></a></p>
<p>From equation (7) it is clear that the short circuit ratio is equal to the reciprocal of the per-unit value of the direct axis synchronous reactance.</p>
<p>In a saturated magnetic circuit, the value of X<sub>d</sub> depends upon the degree of saturation.</p>
<h2>Significance of Short Circuit Ratio (SCR)</h2>
<p><strong>Short Circuit Ratio</strong> is an important factor of the synchronous machine. It affects the operating characteristics, physical size, and cost of the machine. The large variation in the terminal voltage with a change in load takes place for the lower value of the short circuit ratio of a synchronous generator. To keep the terminal voltage constant, the field current (I<sub>f</sub>) has to be varied over a wide range.</p>
<p>For the small value of the short circuit ratio (SCR), the synchronizing power is small. As the synchronizing power keeps the machine in synchronism, a lower value of the SCR has a low stability limit. In other words, a machine with a low SCR is less stable when operating in parallel with the other generators.</p>
<p>A synchronous machine with a high value of SCR had a better voltage regulation and improved steady-state stability limit, but the short circuit fault current in the armature is high. It also affects the size and cost of the machine.</p>
<p>The excitation voltage of the synchronous machine is given by the equation:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-8-compressor.jpg" rel="attachment wp-att-2719"><img decoding="async" loading="lazy" class="size-full wp-image-2719 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-8-compressor.jpg" alt="Short-Circuit-Ratio-of-Synchronous-Machine-eq-8" width="201" height="59" /></a></p>
<p>For the same value of Tph Excitation voltage is directly proportional to the field flux per pole.<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-9-compressor.jpg" rel="attachment wp-att-2720"><img decoding="async" loading="lazy" class="size-full wp-image-2720 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-9-compressor.jpg" alt="Short-Circuit-Ratio-of-Synchronous-Machine-eq-9" width="276" height="79" /></a></p>
<p>The synchronous inductance is given as:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-10-compressor.jpg" rel="attachment wp-att-2721"><img decoding="async" loading="lazy" class="size-full wp-image-2721 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-10-compressor.jpg" alt="Short-Circuit-Ratio-of-Synchronous-Machine-eq-10" width="275" height="76" /></a></p>
<p>Therefore,<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-11-compressor.jpg" rel="attachment wp-att-2722"><img decoding="async" loading="lazy" class="size-full wp-image-2722 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Short-Circuit-Ratio-of-Synchronous-Machine-eq-11-compressor.jpg" alt="Short-Circuit-Ratio-of-Synchronous-Machine-eq-11" width="133" height="69" /></a></p>
<p>Hence, the short circuit ratio is directly proportional to the air gap reluctance or air gap length.</p>
<p>If the length of the air gap is increased, the SCR can be increased. With the increase in the air gap length, the field MMF is to be increased for the same value of excitation voltage (E<sub>f</sub>). Hence, to increase the value of field MMF either field current or the number of field turns has to be increased. All this requires a greater height of field poles and, as a result, the overall diameter of the machine increases.</p>
<p>Thus, a conclusion is that the large value of SCR will increase the size, weight, and cost of the machine.</p>
<p>The typical values of the SCR for different types of machines are as follows:-</p>
<ul>
<li>For <strong>cylindrical rotor</strong> machines, the value of SCR lies between 0.5 to 0.9.</li>
<li>In the case of the <strong>Salient-pole machine</strong>, it lies between 1 to 1.5 and</li>
<li>For <strong>synchronous compensators</strong>, it is 0.4.</li>
</ul>
<p>This is all about Short Circuit Ratio of a Synchronous Machine.</p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/short-circuit-ratio-of-a-synchronous-machine.html">Short Circuit Ratio of a Synchronous Machine</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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		<title>Generator Synchronization</title>
		<link>https://circuitglobe.com/generator-synchronization.html</link>
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		<dc:creator><![CDATA[bhakti]]></dc:creator>
		<pubDate>Sat, 16 Jan 2016 08:35:09 +0000</pubDate>
				<category><![CDATA[Synchronous Machines]]></category>
		<guid isPermaLink="false">https://circuitglobe.com/?p=2701</guid>

					<description><![CDATA[<p>A stationary generator must not be connected to live Busbars because the induced EMF is zero at standstill resulting in a short circuit. The Synchronisation procedure and the equipment for checking it are the same whether one alternator is to be connected in parallel with another alternator, or an alternator is to be connected to &#8230;</p>
<p class="read-more"> <a class="" href="https://circuitglobe.com/generator-synchronization.html"> <span class="screen-reader-text">Generator Synchronization</span> Read More »</a></p>
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]]></description>
										<content:encoded><![CDATA[<p>A stationary generator must not be connected to live Busbars because the induced EMF is zero at standstill resulting in a short circuit. The <strong>Synchronisation</strong> procedure and the equipment for checking it are the same whether one alternator is to be connected in parallel with another alternator, or an alternator is to be connected to the infinite bus.</p>
<p><strong>Contents:</strong></p>
<ul>
<li><a href="#SynchronizationbySynchronizinglamps">Synchronisation by Synchronising lamps</a></li>
<li><a href="#AdvantagesoftheDarkLampMethod">Advantages of the Dark Lamp Method</a></li>
<li><a href="#DisadvantagesoftheDarkLampMethod">Disadvantages of the Dark Lamp Method</a></li>
<li><a href="#ThreeBrightLampMethod">Three Bright Lamp Method</a></li>
<li><a href="#TwoBrightOneDarkLampMethod">Two Bright One Dark Lamp Method</a></li>
</ul>
<p>The following methods are used for synchronization.<br />
<a name="SynchronizationbySynchronizinglamps"></a></p>
<h2>Synchronisation by Synchronising lamps</h2>
<p>A set of three synchronizing lamps can be used to check the conditions for paralleling or synchronization of the incoming machine with the other machine. A dark lamp method along with a voltmeter used for synchronizing is shown below. This method is used for low-power machines.</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/generator-synchronization-figure-1-compressor.jpg" rel="attachment wp-att-2702"><img decoding="async" loading="lazy" class="aligncenter wp-image-2702" src="https://circuitglobe.com/wp-content/uploads/2016/01/generator-synchronization-figure-1-compressor.jpg" alt="generator-synchronization-figure-1" width="496" height="534" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/generator-synchronization-figure-1-compressor.jpg 774w, https://circuitglobe.com/wp-content/uploads/2016/01/generator-synchronization-figure-1-compressor-278x300.jpg 278w, https://circuitglobe.com/wp-content/uploads/2016/01/generator-synchronization-figure-1-compressor-768x828.jpg 768w" sizes="(max-width: 496px) 100vw, 496px" /></a></p>
<p>The prime mover of the incoming machine is started and brought nearer to its rated speed. A field current of the incoming machine is adjusted in such a way so that it becomes equal to the bus voltage. The flicker of the three lamps occurs at a rate that is equal to the difference in the frequencies of the incoming machine and the bus. All the lamps will glow and off at the same time if the phases are properly connected. If this condition does not satisfy, then the phase sequence is not connected correctly.</p>
<p>Thus, in order to connect the machine in the correct phase sequence, two leads to the line of the incoming machine should be interchanged. The frequency of the incoming machine is adjusted until the lamp flicker at a slow rate. The flicker rate should be less than one dark period per second. After finally adjusting the incoming voltage, the synchronizing switch is closed in the middle of their dark period.<br />
<a name="AdvantagesoftheDarkLampMethod"></a></p>
<h3>Advantages of the Dark Lamp Method</h3>
<ul>
<li>This method is cheaper.</li>
<li>The correct phase sequence is easily determined.</li>
</ul>
<p><a name="DisadvantagesoftheDarkLampMethod"></a></p>
<h3>Disadvantages of the Dark Lamp Method</h3>
<ul>
<li>The lamp becomes dark at about half of its rated voltage. Hence, it is possible that the synchronizing switch might be switched off even when there is a phase difference between the machine.</li>
<li>The filament of the lamp might burn out.</li>
<li>The flicker of the lamps does not indicate which lamp has the higher frequency.</li>
</ul>
<p><a name="ThreeBrightLampMethod"></a></p>
<h2>Three Bright Lamp Method</h2>
<p>In this method, the lamps are connected across the phases such as A<sub>1</sub> is connected to B<sub>2</sub>, B<sub>1</sub> is connected to C<sub>2,</sub> and C<sub>1</sub> is connected to A<sub>2</sub>. If all the three lamps get bright and dark together, this means that the phase sequence is correct. The correct instant of closing the synchronizing switch is in the middle of the bright period.<br />
<a name="TwoBrightOneDarkLampMethod"></a></p>
<h2>Two Bright One Dark Lamp Method</h2>
<p>In this method, one lamp is connected between corresponding phases while the two others are cross-connected between the other two phases as shown in the figure below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/GENERATOR-SYNCHRONIZATION-FIG-2-compressor.jpg" rel="attachment wp-att-2703"><img decoding="async" loading="lazy" class="aligncenter wp-image-2703" src="https://circuitglobe.com/wp-content/uploads/2016/01/GENERATOR-SYNCHRONIZATION-FIG-2-compressor.jpg" alt="GENERATOR-SYNCHRONIZATION-FIG-2" width="365" height="378" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/GENERATOR-SYNCHRONIZATION-FIG-2-compressor.jpg 465w, https://circuitglobe.com/wp-content/uploads/2016/01/GENERATOR-SYNCHRONIZATION-FIG-2-compressor-289x300.jpg 289w" sizes="(max-width: 365px) 100vw, 365px" /></a></p>
<p>Here, A<sub>1</sub> is connected to A<sub>2</sub>, B<sub>1</sub> to C<sub>2,</sub> and C<sub>1</sub> to B<sub>2</sub>. The prime mover of the incoming machine is started and brought up to its rated speed. The excitation of the incoming machine is adjusted in such a way that the incoming machine induces the voltage E<sub>A1</sub>, E<sub>B2</sub>, E<sub>C3</sub>, which is equal to the Busbar voltages V<sub>A1</sub>, V<sub>B1</sub> and V<sub>C1</sub>. The diagram is shown below.</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/GENERATOR-SYNCHRONIZATION-FIG-3-compressor.jpg" rel="attachment wp-att-2704"><img decoding="async" loading="lazy" class="aligncenter wp-image-2704" src="https://circuitglobe.com/wp-content/uploads/2016/01/GENERATOR-SYNCHRONIZATION-FIG-3-compressor.jpg" alt="GENERATOR-SYNCHRONIZATION-FIG-3" width="401" height="414" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/GENERATOR-SYNCHRONIZATION-FIG-3-compressor.jpg 593w, https://circuitglobe.com/wp-content/uploads/2016/01/GENERATOR-SYNCHRONIZATION-FIG-3-compressor-291x300.jpg 291w" sizes="(max-width: 401px) 100vw, 401px" /></a></p>
<p>The correct moment to close the switch is obtained at the instant when the straight connected lamp is dark, and the connected cross lamps are equally bright. If the phase sequence is incorrect, no such instant will take place, and all the lamps will be dark simultaneously.</p>
<p>The direction of rotation of the incoming machine is changed by interchanging the two lines of the machine. Since the dark range of the lamp extends to a considerable voltage range, a voltmeter V<sub>1</sub> is connected across the straight lamp. The synchronizing switch is closed when the voltmeter reading is zero.</p>
<p>Thus, the incoming machine is now floating on the Busbar and is ready to take up the load as a generator. If the prime mover is disconnected, it behaves as a motor. For paralleling small machines in power stations, three lamps along with the synchroscope are used. For synchronizing very large machines in power stations, the whole procedure is performed automatically by the computer.</p>
<p><strong>Also See:</strong> <a href="/synchroscope-synchronizing.html">Synchroscope Synchronizing</a></p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/generator-synchronization.html">Generator Synchronization</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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		<title>Capability Curve of a Synchronous Generator</title>
		<link>https://circuitglobe.com/capability-curve-of-a-synchronous-generator.html</link>
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		<dc:creator><![CDATA[bhakti]]></dc:creator>
		<pubDate>Fri, 15 Jan 2016 11:16:41 +0000</pubDate>
				<category><![CDATA[Synchronous Machines]]></category>
		<guid isPermaLink="false">https://circuitglobe.com/?p=2690</guid>

					<description><![CDATA[<p>The Capability Curve of a Synchronous Generator defines a boundary within which the machine can operate safely. It is also known as Operating Charts or Capability Charts. The permissible region of operation is restricted to the following points given below: The MVA loading should not exceed the generator rating. This limit is determined by the &#8230;</p>
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]]></description>
										<content:encoded><![CDATA[<p>The <strong>Capability Curve</strong> of a Synchronous Generator defines a boundary within which the machine can operate safely. It is also known as <strong>Operating Charts</strong> or <strong>Capability Charts</strong>. The permissible region of operation is restricted to the following points given below:</p>
<ul>
<li>The MVA loading should not exceed the generator rating. This limit is determined by the armature of the stator heating by the armature current.</li>
<li>The MW loading should not exceed the rating of the prime mover.</li>
<li>The field current should not be allowed to exceed a specified value determined by the heating of the field.</li>
<li>For steady-state or stable operation, the load angle δ must be less than 90 degrees. The theoretical stability limit of the stable condition occurs when δ = 90⁰.</li>
</ul>
<p>The capability curve is based upon the phasor diagram of the synchronous machine. The<strong> phasor diagram</strong> of a cylindrical rotor alternator at lagging power factor is shown below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-1-compressor.jpg" rel="attachment wp-att-2692"><img decoding="async" loading="lazy" class="aligncenter wp-image-2692" src="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-1-compressor.jpg" alt="capability-curve-of-a-synchronous-generator-fig-1" width="467" height="390" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-1-compressor.jpg 805w, https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-1-compressor-300x250.jpg 300w, https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-1-compressor-768x641.jpg 768w" sizes="(max-width: 467px) 100vw, 467px" /></a></p>
<p>For simplicity, the armature resistance and saturation are assumed to be negligible. The machine is assumed to be connected to constant voltage busbars so that the voltage V<sub>p </sub>is constant. The length O’O (= V<sub>p</sub>) is fixed. The axes Ox and Oy are drawn with their origin O at the tip of V<sub>p</sub>.</p>
<p>From the phasor diagram,<a href="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-synchronous-generator-eq-1-compressor.jpg" rel="attachment wp-att-2691"><img decoding="async" loading="lazy" class="size-full wp-image-2691 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-synchronous-generator-eq-1-compressor.jpg" alt="capability-curve-of-synchronous-generator-eq-1" width="436" height="98" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-synchronous-generator-eq-1-compressor.jpg 436w, https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-synchronous-generator-eq-1-compressor-300x67.jpg 300w" sizes="(max-width: 436px) 100vw, 436px" /></a></p>
<p>The real power output of the generator is given as:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-synchronous-generator-eq-2-compressor.jpg" rel="attachment wp-att-2693"><img decoding="async" loading="lazy" class="size-full wp-image-2693 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-synchronous-generator-eq-2-compressor.jpg" alt="capability-curve-of-synchronous-generator-eq-2" width="174" height="45" /></a></p>
<p>The reactive power output of the generator is given as<a href="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-synchronous-generator-eq-3-compressor.jpg" rel="attachment wp-att-2694">:<img decoding="async" loading="lazy" class="size-full wp-image-2694 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-synchronous-generator-eq-3-compressor.jpg" alt="capability-curve-of-synchronous-generator-eq-3" width="170" height="46" /></a></p>
<p>A typical capability curve for a cylindrical rotor generator is shown below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-2-compressor.jpg" rel="attachment wp-att-2696"><img decoding="async" loading="lazy" class="aligncenter wp-image-2696" src="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-2-compressor.jpg" alt="capability-curve-of-a-synchronous-generator-fig-2" width="515" height="542" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-2-compressor.jpg 715w, https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-2-compressor-285x300.jpg 285w" sizes="(max-width: 515px) 100vw, 515px" /></a></p>
<p>&nbsp;</p>
<p>The curve is plotted on the S-plane, where P is the vertical axis and Q is the horizontal axis. For constant power Ia and volt-amperes S = VA, the locus is a circle with a center at O and radius OB (= 3 V<sub>p</sub> I<sub>a</sub>). Constant P operation lies on a line parallel to Q axis. The constant excitation locus is a circle with center O’ and radius O’B ( = 3 V<sub>p </sub>E<sub>f</sub>/X<sub>s</sub>). Constant power factor lines are straight radial lines from O.</p>
<p>For excitation E<sub>f </sub>equal to zero, the armature current is given as:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-synchronous-generator-eq-4-compressor.jpg" rel="attachment wp-att-2697"><img decoding="async" loading="lazy" class="size-full wp-image-2697 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-synchronous-generator-eq-4-compressor.jpg" alt="capability-curve-of-synchronous-generator-eq-4" width="99" height="69" /></a></p>
<p>= short circuit current at rated voltage</p>
<p>= OO’</p>
<p>The theoretical stability limit is a straight line O’M at right angles to O’O at O’. Here δ = 90⁰. Between a and b, the operation of the alternator is limited by the maximum field current, and a circle of radius (3 V E<sub>f</sub>/ X<sub>s</sub>) with center O’. Between b and c, the operation is limited by the MVA limit. Here I<sub>a</sub> is the maximum permissible armature current. Between c and d, the operation is limited by the power of the prime mover. Between d and e, the operation is limited by the practical stability limit.</p>
<p>The theoretical limit of stability occurs where δ = 90⁰. But there must be a safety margin between the theoretical limit and that used in practice. The practical limit is usually taken 10% less than the theoretical stability limit. The complete operating zone of the alternator is <strong>abcdkOa</strong>. The operation of the alternator within this area is safe from the standpoints of heating and stability. Once an operating point is located within this area, the desired power P, S, Q i.e., Current, power factor, and excitation are found.</p>
<p>Consider the figure given below.</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-3-compressor-1.jpg" rel="attachment wp-att-2698"><img decoding="async" loading="lazy" class="aligncenter wp-image-2698" src="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-3-compressor-1.jpg" alt="capability-curve-of-a-synchronous-generator-fig-3" width="460" height="440" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-3-compressor-1.jpg 705w, https://circuitglobe.com/wp-content/uploads/2016/01/capability-curve-of-a-synchronous-generator-fig-3-compressor-1-300x287.jpg 300w" sizes="(max-width: 460px) 100vw, 460px" /></a>Here an operating point F is considered, and the following information is given:</p>
<ul>
<li>If point F is inside the capability curve, the machine will not be overheated and will not be likely to fall out of synchronism.</li>
<li>A line from F to the origin O’ of the I<sub>f</sub> is at an angle δ from the axis.</li>
<li>A line FG through F parallel to O’Oa give power equal to OG.</li>
<li>A line from F to the origin O of the Q axis gives the power factor angle ϕ from the vertical axis. i.e., ∠FOG = ϕ</li>
<li>The armature current I<sub>a</sub> is given by OF.</li>
<li>The VA output is given by (OF x operating voltage)</li>
<li>The VAr output is given by GF x output voltage</li>
<li>O’F gives the excitation E<sub>f</sub>.</li>
</ul>
<p>This is all about capability curve.</p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/capability-curve-of-a-synchronous-generator.html">Capability Curve of a Synchronous Generator</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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		<title>Hunting in a Synchronous Motor</title>
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		<dc:creator><![CDATA[bhakti]]></dc:creator>
		<pubDate>Fri, 15 Jan 2016 08:32:07 +0000</pubDate>
				<category><![CDATA[Synchronous Machines]]></category>
		<guid isPermaLink="false">https://circuitglobe.com/?p=2683</guid>

					<description><![CDATA[<p>The phenomenon of oscillation of the rotor about its final equilibrium position is called Hunting. On the sudden application of load, the rotor search for its new equilibrium position, and this process is known as Hunting. The Hunting process occurs in a synchronous motor as well as in synchronous generators if an abrupt change in &#8230;</p>
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<p>The post <a rel="nofollow" href="https://circuitglobe.com/hunting-in-synchronous-motor.html">Hunting in a Synchronous Motor</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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										<content:encoded><![CDATA[<p style="text-align: justify;">The phenomenon of oscillation of the rotor about its final equilibrium position is called <strong>Hunting.</strong> On the sudden application of load, the rotor search for its new equilibrium position, and this process is known as <strong>Hunting</strong>. The Hunting process occurs in a synchronous motor as well as in synchronous generators if an abrupt change in load occurs.</p>
<p style="text-align: justify;">The steady-state or stable operation of a synchronous motor is a condition of equilibrium. In it, the load torque is equal as well as opposite to the electromagnetic torque. The rotor of the motor runs at synchronous speed in the steady-state condition, maintain a constant value of the torque angle δ. The equilibrium gets disturbed if a sudden change occurs in the load torque. Thus, a resulting torque takes place which changes the speed of the motor. It is given by the equation shown below.<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Hunting-in-synchronous-motor-eq-1-compressor.jpg" rel="attachment wp-att-2684"><img decoding="async" loading="lazy" class="size-full wp-image-2684 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Hunting-in-synchronous-motor-eq-1-compressor.jpg" alt="Hunting-in-synchronous-motor-eq-1" width="320" height="67" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/Hunting-in-synchronous-motor-eq-1-compressor.jpg 320w, https://circuitglobe.com/wp-content/uploads/2016/01/Hunting-in-synchronous-motor-eq-1-compressor-300x63.jpg 300w" sizes="(max-width: 320px) 100vw, 320px" /></a></p>
<p>Where J is the moment of inertia</p>
<p>ω<sub>M</sub> is the angular velocity of the rotor in mechanical units.</p>
<p>The speed of the motor slows down temporarily, and the torque angle δ is sufficiently increased. This is done to restore the torque equilibrium and the synchronous speed when there is a sudden increase in the load torque.</p>
<p>The electromagnetic torque is given by the equation shown below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/Hunting-in-synchronous-motor-eq-2-compressor.jpg" rel="attachment wp-att-2685"><img decoding="async" loading="lazy" class="size-full wp-image-2685 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/Hunting-in-synchronous-motor-eq-2-compressor.jpg" alt="Hunting-in-synchronous-motor-eq-2" width="272" height="70" /></a></p>
<p>If the value of δ is increased, the electromagnetic torque is also increased. As a result, the motor is accelerated. As the rotor reaches the synchronous speed, the torque angle δ is larger than the required value. Here the rotor speed continues to increase beyond the synchronous speed.</p>
<p>As the rotor accelerates above synchronous speed, the torque angle δ decreases. At the point where the motor torque becomes equal to the load torque, the equilibrium is not restored because now the rotor speed is greater than the synchronous speed. Therefore, the rotor continues to swing backward and as a result, the torque angle goes on decreasing.</p>
<p>When the load angle δ becomes less than the required value, the mechanical load becomes greater than the developed power. Therefore, the motor starts to slow down. The load angle starts increasing again. Thus, the rotor starts to swing or oscillates around the synchronous speed.</p>
<p>The motor responds to a decreasing load torque by a temporary increase in speed and a reduction of the torque angle δ. Thus, the rotor swings and rotates around the synchronous speed. Hence, this process of rotation of the rotor speed equal to or around the synchronous speed is known as Hunting. Since, during the rotor oscillation, the phase of the phasor Ef changes about phasor V. Thus, hunting is known as<strong> Phase Swinging.</strong></p>
<h3>Causes of Hunting</h3>
<p>The various causes of hunting are as follows:</p>
<ul>
<li>Sudden changes of load.</li>
<li>Faults were occurring in the system which the generator supplies.</li>
<li>Sudden change in the field current.</li>
<li>Cyclic variations of the load torque.</li>
</ul>
<h3>Effect of Hunting</h3>
<p>The various effects of hunting are as follows:-</p>
<ul>
<li>It can lead to loss of synchronism.</li>
<li>It can cause variations of the supply voltage producing undesirable lamp flicker.</li>
<li>The possibility of Resonance condition increases. If the frequency of the torque component becomes equal to that of the transient oscillations of the synchronous machine, resonance may take place.</li>
<li>Large mechanical stresses may develop in the rotor shaft.</li>
<li>The machine losses increase and the temperature of the machine rises.</li>
</ul>
<h3>Reduction of Hunting</h3>
<p>The following technique given below is used to reduce the phenomenon of hunting.</p>
<ul>
<li>Use of damper windings</li>
<li>Uses of flywheels</li>
</ul>
<p>The prime mover is provided with a large and heavy flywheel. This increases the inertia of the prime mover and helps in maintaining the rotor speed constant.</p>
<ul>
<li>By designing synchronous machines with suitable synchronising power coefficients.</li>
</ul>
<p>This is all for hunting in synchronous motors.</p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/hunting-in-synchronous-motor.html">Hunting in a Synchronous Motor</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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		<title>V Curve of a Synchronous Motor</title>
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		<dc:creator><![CDATA[bhakti]]></dc:creator>
		<pubDate>Thu, 14 Jan 2016 11:15:56 +0000</pubDate>
				<category><![CDATA[Synchronous Machines]]></category>
		<guid isPermaLink="false">https://circuitglobe.com/?p=2676</guid>

					<description><![CDATA[<p>V curve is a plot of the stator current versus field current for different constant loads. The Graph plotted between the armature current Ia and field current If at no load the curve is obtained known as V Curve. Since the shape of these curves is similar to the letter “V”, thus they are called &#8230;</p>
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<p>The post <a rel="nofollow" href="https://circuitglobe.com/v-curve-of-synchronous-motor.html">V Curve of a Synchronous Motor</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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										<content:encoded><![CDATA[<p><strong>V curve</strong> is a plot of the stator current versus field current for different constant loads. The Graph plotted between the<strong> armature current I<sub>a</sub></strong> and <strong>field current I</strong><sub>f</sub> at no load the curve is obtained known as <strong>V Curve</strong>. Since the shape of these curves is similar to the letter “V”, thus they are called the V curve of a synchronous motor.</p>
<p>The power factor of the synchronous motor can be controlled by varying the field current I<sub>f</sub>. As we know that the armature current I<sub>a</sub> changes with the change in the field current I<sub>f</sub>. Let us assume that the motor is running at NO load. If the field current is increased from this small value, the armature current Ia decreases until the armature current becomes minimum. At this minimum point, the motor is operating at a unity power factor. The motor operates at a lagging power factor until it reaches up to this point of operation.</p>
<p>If now, the field current is increased further, the armature current increases and the motor starts operating as a leading power factor. The graph drawn between armature current and field current is known as the V curve. If this procedure is repeated for various increased loads, a family of curves is obtained.</p>
<p>The<strong> V curves</strong> of a synchronous motor are shown below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/V-CURVE-OF-SYNCHRONOUS-MOTOR-FIG-1-compressor.jpg" rel="attachment wp-att-2677"><img decoding="async" loading="lazy" class="aligncenter wp-image-2677" src="https://circuitglobe.com/wp-content/uploads/2016/01/V-CURVE-OF-SYNCHRONOUS-MOTOR-FIG-1-compressor.jpg" alt="V-CURVE-OF-SYNCHRONOUS-MOTOR-FIG-1" width="461" height="496" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/V-CURVE-OF-SYNCHRONOUS-MOTOR-FIG-1-compressor.jpg 668w, https://circuitglobe.com/wp-content/uploads/2016/01/V-CURVE-OF-SYNCHRONOUS-MOTOR-FIG-1-compressor-279x300.jpg 279w" sizes="(max-width: 461px) 100vw, 461px" /></a> The point at which the unity power factor occurs is at the point where the armature current is minimum. The curve connecting the lowest points of all the V curves for various power levels is called the<strong> Unity Power Factor Compounding Curve</strong>. The compounding curves for 0.8 power factor lagging and 0.8 power factor leading are shown in the figure above by a red dotted line.</p>
<p>The loci of constant power factor points on the V curves are called <strong>Compounding Curves</strong>. It shows the manner in which the field current should be varied in order to maintain a constant power factor under changing load. Points on the right and left of the unity power factor corresponds to the over-excitation and leading current and under excitation and lagging current respectively.</p>
<p>The V curves are useful in adjusting the field current. Increasing the field current, If beyond the level for minimum armature current results in leading power factor. Similarly decreasing the field current below the minimum armature current results in a lagging power factor. It is seen that the field current for the unity power factor at full load is more than the field current for unity power factor at no load.</p>
<p>The figure below shows the graph between power factor and field current at the different loads.<a href="https://circuitglobe.com/wp-content/uploads/2016/01/V-CURVE-OF-SYNCHRONOUS-MOTOR-FIG-2-compressor.jpg" rel="attachment wp-att-2678"><img decoding="async" loading="lazy" class="aligncenter wp-image-2678" src="https://circuitglobe.com/wp-content/uploads/2016/01/V-CURVE-OF-SYNCHRONOUS-MOTOR-FIG-2-compressor.jpg" alt="V-CURVE-OF-SYNCHRONOUS-MOTOR-FIG-2" width="475" height="372" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/V-CURVE-OF-SYNCHRONOUS-MOTOR-FIG-2-compressor.jpg 778w, https://circuitglobe.com/wp-content/uploads/2016/01/V-CURVE-OF-SYNCHRONOUS-MOTOR-FIG-2-compressor-300x235.jpg 300w, https://circuitglobe.com/wp-content/uploads/2016/01/V-CURVE-OF-SYNCHRONOUS-MOTOR-FIG-2-compressor-768x601.jpg 768w" sizes="(max-width: 475px) 100vw, 475px" /></a></p>
<p>It is clear from the above figure that, if the synchronous motor at full load is operating at unity power factor, then removal of the shaft load causes the motor to operate at a leading power factor.</p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/v-curve-of-synchronous-motor.html">V Curve of a Synchronous Motor</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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		<title>Synchronizing Power and Torque Coefficient</title>
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		<dc:creator><![CDATA[bhakti]]></dc:creator>
		<pubDate>Thu, 14 Jan 2016 09:34:15 +0000</pubDate>
				<category><![CDATA[Synchronous Machines]]></category>
		<guid isPermaLink="false">https://circuitglobe.com/?p=2660</guid>

					<description><![CDATA[<p>Definition: &#8211; Synchronizing Power is defined as the varying of the synchronous power P on varying in the load angle δ. It is also called the Stiffness of Coupling, Stability or Rigidity factor. It is represented as Psyn. A synchronous machine, whether a generator or a motor, when synchronized to infinite busbars has an inherent &#8230;</p>
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										<content:encoded><![CDATA[<p><strong>Definition: &#8211; Synchronizing Power</strong> is defined as the varying of the synchronous power P on varying in the load angle δ. It is also called the <strong>Stiffness of Coupling</strong>, <strong>Stability</strong> or <strong>Rigidity factor</strong>. It is represented as <strong>P<sub>syn</sub></strong>. A synchronous machine, whether a generator or a motor, when synchronized to infinite busbars has an inherent tendency to remain in<strong> synchronism</strong>.</p>
<p>Consider asynchronous generator transferring a steady power P<sub>a</sub> at a steady load angle δ<sub>0</sub>. Suppose that, due to a transient disturbance, the rotor of the generator accelerates, resulting from an increase in the load angle by dδ. The operating point of the machine shifts to a new constant power line and the load on the machine increases to P<sub>a</sub> + δP. The steady power input of the machine does not change, and the additional load which is added decreases the speed of the machine and brings it back to synchronism.</p>
<p>Similarly, if due to a transient disturbance, the rotor of the machine retards resulting a decrease in the load angle. The operating point of the machine shifts to a new constant power line and the load on the machine decreases to (P<sub>a</sub> – δP). Since the input remains unchanged, the reduction in load accelerates the rotor. The machine again comes in synchronism.</p>
<p>The effectiveness of this correcting action depends on the change in power transfer for a given change in load angle. The measure of effectiveness is given by <strong>Synchronising</strong> <strong>Power Coefficient</strong>.<a href="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-1-compressor.jpg" rel="attachment wp-att-2661"><img decoding="async" loading="lazy" class="size-full wp-image-2661 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-1-compressor.jpg" alt="SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-1" width="223" height="65" /></a></p>
<p>Power output per phase of the cylindrical rotor generator synchronizing torque coefficient<a href="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-3-compressor.jpg" rel="attachment wp-att-2663"><img decoding="async" loading="lazy" class="size-full wp-image-2663 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-3-compressor.jpg" alt="SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-3" width="407" height="148" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-3-compressor.jpg 407w, https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-3-compressor-300x109.jpg 300w" sizes="(max-width: 407px) 100vw, 407px" /></a></p>
<p>In many synchronous machines Xs &gt;&gt; R. Therefore, for a cylindrical rotor machine, neglecting saturation and stator resistance equation (3) and (5) become<a href="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-4-compressor.jpg" rel="attachment wp-att-2664"><img decoding="async" loading="lazy" class="size-full wp-image-2664 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-4-compressor.jpg" alt="SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-4" width="339" height="147" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-4-compressor.jpg 339w, https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-4-compressor-300x130.jpg 300w" sizes="(max-width: 339px) 100vw, 339px" /></a></p>
<p>For a salient pole machine<a href="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-5-compressor.jpg" rel="attachment wp-att-2665"><img decoding="async" loading="lazy" class="size-full wp-image-2665 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-5-compressor.jpg" alt="SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-5" width="497" height="151" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-5-compressor.jpg 497w, https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-5-compressor-300x91.jpg 300w" sizes="(max-width: 497px) 100vw, 497px" /></a></p>
<h2>Unit of Synchronizing Power Coefficient P<sub>syn</sub></h2>
<p>The<strong> synchronizing power coefficient</strong> is expressed in watts per electrical radian.</p>
<p>Therefore,<a href="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-6-compressor.jpg" rel="attachment wp-att-2666"><img decoding="async" loading="lazy" class="size-full wp-image-2666 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-6-compressor.jpg" alt="SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-6" width="424" height="80" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-6-compressor.jpg 424w, https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-6-compressor-300x57.jpg 300w" sizes="(max-width: 424px) 100vw, 424px" /></a></p>
<p>Since, π radians = 180⁰</p>
<p>1 radian = 180/π degrees<a href="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-7-compressor.jpg" rel="attachment wp-att-2667"><img decoding="async" loading="lazy" class="size-full wp-image-2667 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-7-compressor.jpg" alt="SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-7" width="537" height="163" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-7-compressor.jpg 537w, https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-7-compressor-300x91.jpg 300w" sizes="(max-width: 537px) 100vw, 537px" /></a></p>
<p>If P is the total number of pair of poles of the machine.<a href="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-8-compressor.jpg" rel="attachment wp-att-2668"><img decoding="async" loading="lazy" class="size-full wp-image-2668 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-8-compressor.jpg" alt="SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-8" width="257" height="53" /></a></p>
<p>Synchronising Power Coefficient per mechanical radian is given by the equation shown below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-9-compressor.jpg" rel="attachment wp-att-2669"><img decoding="async" loading="lazy" class="size-full wp-image-2669 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-9-compressor.jpg" alt="SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-9" width="333" height="63" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-9-compressor.jpg 333w, https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-9-compressor-300x57.jpg 300w" sizes="(max-width: 333px) 100vw, 333px" /></a></p>
<p>Synchronising Power Coefficient per mechanical degree is given as:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-10-compressor.jpg" rel="attachment wp-att-2670"><img decoding="async" loading="lazy" class="size-full wp-image-2670 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-10-compressor.jpg" alt="SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-10" width="354" height="72" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-10-compressor.jpg 354w, https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-10-compressor-300x61.jpg 300w" sizes="(max-width: 354px) 100vw, 354px" /></a></p>
<h2>Synchronising Torque Coefficient</h2>
<p><strong>Synchronising Torque Coefficient</strong> gives rise to the synchronising torque coefficient at synchronous speed. That is, the Synchronizing Torque is the torque at which synchronous speed gives the synchronising power. If <strong>Ʈ<sub>syn</sub></strong> is the synchronising torque coefficient then the equation is given as shown below:<a href="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-11-compressor.jpg" rel="attachment wp-att-2671"><img decoding="async" loading="lazy" class="size-full wp-image-2671 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-11-compressor.jpg" alt="SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-11" width="574" height="140" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-11-compressor.jpg 574w, https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-11-compressor-300x73.jpg 300w" sizes="(max-width: 574px) 100vw, 574px" /></a> Where,</p>
<ul>
<li>m is the number of phases of the machine</li>
<li>ω<sub>s</sub> = 2 π n<sub>s</sub></li>
<li>n<sub>s </sub> is the synchronous speed in revolution per second</li>
</ul>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-12-compressor.jpg" rel="attachment wp-att-2672"><img decoding="async" loading="lazy" class="size-full wp-image-2672 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-12-compressor.jpg" alt="SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-12" width="340" height="72" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-12-compressor.jpg 340w, https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-12-compressor-300x64.jpg 300w" sizes="(max-width: 340px) 100vw, 340px" /></a></p>
<h2>Significance of Synchronous Power Coefficient</h2>
<p>The <strong>Synchronous Power Coefficien</strong>t P<sub>syn</sub> is the measure of the stiffness between the rotor and the stator coupling. A large value of P<sub>syn</sub> indicates that the coupling is stiff or rigid. Too rigid a coupling means and the machine will be subjected to shock, with the change of load or supply. These shocks may damage the rotor or the windings. We have,<a href="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-13-compressor.jpg" rel="attachment wp-att-2673"><img decoding="async" loading="lazy" class="size-full wp-image-2673 aligncenter" src="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-13-compressor.jpg" alt="SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-13" width="364" height="152" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-13-compressor.jpg 364w, https://circuitglobe.com/wp-content/uploads/2016/01/SYNCHRONIZING-POWER-AND-TORQUE-COEFFICIENT-EQ-13-compressor-300x125.jpg 300w" sizes="(max-width: 364px) 100vw, 364px" /></a></p>
<p>The above two equations (17) and (18) show that P<sub>syn</sub> is inversely proportional to the synchronous reactance. A machine with large air gaps has relatively small reactance. The synchronous machine with the larger air gap is stiffer than a machine with a smaller air gap. Since P<sub>syn</sub> is directly proportional to E<sub>f</sub>, an overexcited machine is stiffer than an under excited machine.</p>
<p>The restoring action is great when δ = 0, that is at no load. When the value of δ = ± 90⁰, the restoring action is zero. At this condition, the machine is in unstable equilibrium and at a steady-state limit of stability. Therefore, it is impossible to run a machine at the steady-state limit of stability since its ability to resist small changes is zero unless the machine provided with a special fast-acting excitation system.</p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/synchronizing-power-and-torque-coefficient.html">Synchronizing Power and Torque Coefficient</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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		<title>Starting of a Synchronous Motor</title>
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		<dc:creator><![CDATA[bhakti]]></dc:creator>
		<pubDate>Wed, 13 Jan 2016 11:24:13 +0000</pubDate>
				<category><![CDATA[Synchronous Machines]]></category>
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					<description><![CDATA[<p>A synchronous motor is a device that converts the AC into mechanical work at synchronous speed. The starting of the Synchronous Motor does not take place on its own. This means that the Synchronous Motor is not Self Starting. It can be started by the following methods given below: Starting with the help of an &#8230;</p>
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<p>The post <a rel="nofollow" href="https://circuitglobe.com/starting-of-synchronous-motor.html">Starting of a Synchronous Motor</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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										<content:encoded><![CDATA[<p>A synchronous motor is a device that converts the AC into mechanical work at synchronous speed<strong>. </strong>The<strong> starting</strong> of the <strong>Synchronous Motor</strong> does not take place on its own. This means that the Synchronous Motor is <strong>not Self Starting</strong>. It can be started by the following methods given below:</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/starting-of-synchronous-motor-figure-1-compressor.jpg" rel="attachment wp-att-2657"><img decoding="async" loading="lazy" class="aligncenter wp-image-2657" src="https://circuitglobe.com/wp-content/uploads/2016/01/starting-of-synchronous-motor-figure-1-compressor.jpg" alt="starting-of-synchronous-motor-figure-1" width="392" height="307" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/starting-of-synchronous-motor-figure-1-compressor.jpg 492w, https://circuitglobe.com/wp-content/uploads/2016/01/starting-of-synchronous-motor-figure-1-compressor-300x235.jpg 300w" sizes="(max-width: 392px) 100vw, 392px" /></a></p>
<ul>
<li>Starting with the help of an External Prime Mover</li>
<li>Starting with the help of Damper Windings</li>
</ul>
<p>A detailed description of the methods is explained below.</p>
<h2>Motor Starting with an External Prime Mover</h2>
<p>In this method, an <strong>external prime mover</strong> drives the synchronous motor and brings it to synchronous speed. The synchronous machine is then synchronized with the bus bar as a synchronous generator. The prime mover is then disconnected. Once operating in parallel condition, the synchronous machine will work as a motor. Thus, the load can be connected to the synchronous motor.</p>
<p>Since the load is not connected to the synchronous motor before synchronizing, the starting motor has to overcome the inertia of the synchronous motor at no load. Therefore, the rating of the motor which has to be started is much smaller than the rating of the synchronous motor. Now a day, a <strong>Brushless excitation system</strong> is provided on the shafts of the large synchronous motor. These<strong> exciters</strong> are used as starting motors.</p>
<h2>Motor Starting with Damper Windings</h2>
<p><strong>Damper Windings</strong> is the most widely used method to start a synchronous motor. A Damper Winding consists of heavy copper bars inserted in the slots of the pole faces of the rotor as shown in the figure below.</p>
<p><a href="https://circuitglobe.com/wp-content/uploads/2016/01/starting-of-synchronous-motor-fig-2.jpg" rel="attachment wp-att-3355"><img decoding="async" loading="lazy" class="aligncenter wp-image-3355 size-full" src="https://circuitglobe.com/wp-content/uploads/2016/01/starting-of-synchronous-motor-fig-2.jpg" alt="Starting of synchronous machine fig 2" width="422" height="345" srcset="https://circuitglobe.com/wp-content/uploads/2016/01/starting-of-synchronous-motor-fig-2.jpg 422w, https://circuitglobe.com/wp-content/uploads/2016/01/starting-of-synchronous-motor-fig-2-300x245.jpg 300w" sizes="(max-width: 422px) 100vw, 422px" /></a></p>
<p>These copper bars are short-circuited by end rings at both ends of the rotor. Thus, these short-circuited Bars form a squirrel cage winding. When a three phase supply is connected to the stator, the synchronous motor with Damper Winding will start. It works as a three-phase induction motor. As soon as the motor approaches the synchronous speed, the DC excitation is applied to the field windings. As a result, the rotor of the motor will pull into step with the stator magnetic field.</p>
<p>The post <a rel="nofollow" href="https://circuitglobe.com/starting-of-synchronous-motor.html">Starting of a Synchronous Motor</a> appeared first on <a rel="nofollow" href="https://circuitglobe.com">Circuit Globe</a>.</p>
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