{"id":19939,"date":"2022-08-15T07:12:30","date_gmt":"2022-08-15T07:12:30","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=6409"},"modified":"2022-08-15T07:12:30","modified_gmt":"2022-08-15T07:12:30","slug":"phasor-diagram-of-a-synchronous-generator","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/08\/15\/phasor-diagram-of-a-synchronous-generator\/","title":{"rendered":"Phasor Diagram of a Synchronous Generator"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/08\/ppppppppppppppppp.png\" alt=\"\" class=\"wp-image-6410\"\/><\/figure>\n\n\n\n<p>In this article we discuss one of the easiest methods of making a <strong>phasor diagram for a synchronous generator<\/strong>.<\/p>\n\n\n\n<p>Now, let us write the various notations for each quantity at one place, this will help us to understand the phasor diagram more clearly. In this phasor diagram we are going to use:<\/p>\n\n\n\n<ul><li>E<sub>f<\/sub>\u00a0which denotes excitation\u00a0voltage<\/li><li>V<sub>t<\/sub>\u00a0which denotes terminal voltage<\/li><li>I<sub>a<\/sub>\u00a0which denotes the armature\u00a0current<\/li><li>\u03b8 which denotes the phase angle between V<sub>t<\/sub>\u00a0and I<sub>a<\/sub><\/li><li>\u1d2a which denotes the angle between the E<sub>f<\/sub>\u00a0and I<sub>a<\/sub><\/li><li>\u03b4 which denotes the angle between the E<sub>f<\/sub>\u00a0and V<sub>t<\/sub><\/li><li>r<sub>a<\/sub>\u00a0which denotes the armature per phase resistance<\/li><\/ul>\n\n\n\n<p>In order to draw the phasor diagram we will use V<sub>t<\/sub> as reference. Consider these two important points which are written below:<\/p>\n\n\n\n<ol><li>We already know that if a machine is working as a\u00a0synchronous generator\u00a0then direction of I<sub>a<\/sub>\u00a0will be in phase to that of the E<sub>f<\/sub>.<\/li><li>Phasor E<sub>f<\/sub>\u00a0is always ahead of V<sub>t<\/sub>.<\/li><\/ol>\n\n\n\n<p>These two points are necessary for making the <strong>phasor diagram of synchronous generator<\/strong>. Given below is the phasor diagram of synchronous generator:<\/p>\n\n\n\n<p>In this phasor diagram we have drawn the direction of the I<sub>a<\/sub> is in phase with that of the E<sub>f<\/sub> as per the point number 1 mentioned above. Now let us derive expression for the excitation emf in each case. We have three cases that are written below:<\/p>\n\n\n\n<ol><li>Generating operation at lagging power factor.<\/li><li>Generating operation at unity power factor.<\/li><li>Generating operation at leading power factor.<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/images\/lagingunityleading-pf-load.gif\" alt=\"phasor diagram of synchronous generator\" class=\"wp-image-18752\"\/><\/figure>\n\n\n\n<p>Given below are the phasor diagrams for all the operations.<\/p>\n\n\n\n<p>(a) Generating operation at lagging power factor:<\/p>\n\n\n\n<p>We can derive the expression for the E<sub>f<\/sub> by first taking the component of the V<sub>t<\/sub> in the direction of I<sub>a<\/sub>. Component of V<sub>t<\/sub> in the direction of I<sub>a<\/sub> is V<sub>t<\/sub>cos\u0398, hence the total voltage drop is<\/p>\n\n\n\n<p><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/images\/2017\/may\/1496215474.PNG?ezimgfmt=rs:120x21\/rscb38\/ng:webp\/ngcb38\" alt=\"\"><\/p>\n\n\n\n<p>along the I<sub>a<\/sub>.<\/p>\n\n\n\n<p>Similarly we can calculate the voltage drop along the direction perpendicular to I<sub>a<\/sub>. The total voltage drop perpendicular to I<sub>a<\/sub> is<img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/images\/2017\/may\/1496215372.PNG?ezimgfmt=rs:119x20\/rscb38\/ng:webp\/ngcb38\" alt=\"\">. With the help of triangle BOD in the first phasor diagram we can write the expression for E<sub>f<\/sub> as<br><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/machine-equation\/generator-equation\/phasor-diagram-for-synchronous-generator-1.gif\" alt=\"\"><br>(b) Generating operation at unity power factor:<br>Here also we can derive the expression for the E<sub>f<\/sub> by first taking the component of the V<sub>t<\/sub> in the direction of I<sub>a<\/sub>. But in this case the value of theta is zero and hence we have \u1d2a = \u03b4.<\/p>\n\n\n\n<p>With the help of triangle BOD in the second phasor diagram we can directly write the expression for E<sub>f<\/sub> as<br><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/machine-equation\/generator-equation\/phasor-diagram-for-synchronous-generator-2.gif\" alt=\"\"><br>(c) Generating operation at leading power factor:<\/p>\n\n\n\n<p>Component in the direction of I<sub>a<\/sub> is V<sub>t<\/sub>cos\u0398. As the direction of Ia is same to that of the V<sub>t<\/sub> thus the total voltage drop is<\/p>\n\n\n\n<p><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/images\/2017\/may\/1496215474.PNG?ezimgfmt=rs:120x21\/rscb38\/ng:webp\/ngcb38\" alt=\"\">.<\/p>\n\n\n\n<p>Similarly we can write expression for the voltage drop along the direction perpendicular to I<sub>a<\/sub>. The total voltage drop comes out to be<img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/images\/2017\/may\/1496215738.PNG?ezimgfmt=rs:124x19\/rscb38\/ng:webp\/ngcb38\" alt=\"\">. With the help of triangle BOD in the first phasor diagram we can write the expression for E<sub>f<\/sub> as<br><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/machine-equation\/generator-equation\/phasor-diagram-for-synchronous-generator-3.gif\" alt=\"\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this article we discuss one of the easiest methods of making a phasor diagram for a synchronous generator. Now, let us write the various notations for each quantity at one place, this will help us to understand the phasor diagram more clearly. In this phasor diagram we are going to use: Ef\u00a0which denotes excitation\u00a0voltage [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[477],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/19939"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=19939"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/19939\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=19939"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=19939"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=19939"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}