{"id":19934,"date":"2022-08-15T05:59:14","date_gmt":"2022-08-15T05:59:14","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=6394"},"modified":"2022-08-15T05:59:14","modified_gmt":"2022-08-15T05:59:14","slug":"equt-circuit-of-trans-referred-to-primary-and-secondary","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/08\/15\/equt-circuit-of-trans-referred-to-primary-and-secondary\/","title":{"rendered":"Equt. Circuit of Trans. referred to Primary and Secondary"},"content":{"rendered":"\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What is the Equivalent Circuit of a Transformer?<\/h2>\n\n\n\n<p>The equivalent circuit diagram of a transformer is a simplified circuit in which the impedance, resistance and leakage reactance of the transformer can be more easily calculated.<\/p>\n\n\n\n<p>The equivalent impedance of transformer is an important parameter to be calculated. This calculation requires the equivalent circuit of transformer referred to the primary or equivalent circuit of transformer referred to secondary sides respectively. Percentage impedance is also a very essential parameter of the transformer.<\/p>\n\n\n\n<p>Special attention is to be given to this parameter during installing a transformer in an existing electrical power system. Percentage impedance of different power transformers should be properly matched during parallel operation of power transformers.<\/p>\n\n\n\n<p>The percentage impedance can be derived from the equivalent impedance of the transformer so, it can be said that the equivalent circuit of the transformer is also required during the calculation of the % impedance.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Equivalent Circuit of Transformer Referred to Primary<\/h2>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/wp-content\/uploads\/2013\/03\/vector-diagram-of-transformer-on-load.gif\" alt=\"vector diagram of transformer on load\" class=\"wp-image-22353\"\/><\/figure>\n\n\n\n<p>For drawing equivalent circuit of transformer referred to primary, first we have to establish general equivalent circuit of transformer then, we will modify it for referring from primary side. For doing this, first we need to recall the complete vector diagram of a transformer which is shown in the figure below.<br><br>Let us consider the transformation ratio be,<br><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/machine-equation\/transformer-equation\/equivalent-circuit-of-transformer-referred-to-primary-and-secondary-1.gif\" alt=\"\"><br>In the figure above, the applied voltage to the primary is V<sub>1<\/sub> and voltage across the primary winding is E<sub>1<\/sub>. Total current supplied to primary is I<sub>1<\/sub>. So the voltage V<sub>1<\/sub> applied to the primary is partly dropped by I<sub>1<\/sub>Z<sub>1<\/sub> or I<sub>1<\/sub>R<sub>1<\/sub> + j.I<sub>1<\/sub>X<sub>1<\/sub> before it appears across primary winding.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/wp-content\/uploads\/2013\/03\/equivalent-circuit.gif\" alt=\"equivalent circuit of transformer\" class=\"wp-image-22356\"\/><\/figure>\n\n\n\n<p>The voltage appeared across winding is countered by primary induced emf E<sub>1<\/sub>. So voltage equation of this portion of the transformer can be written as,<br><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/machine-equation\/transformer-equation\/equivalent-circuit-of-transformer-referred-to-primary-and-secondary-2.gif\" alt=\"\"><br>The equivalent circuit for that equation can be drawn as below,<br><br>From the vector diagram above, it is found that the total primary current I<sub>1<\/sub> has two components, one is no \u2013 load component I<sub>o<\/sub> and the other is load component I<sub>2<\/sub>\u2032. As this primary current has two components or branches, so there must be a parallel path with primary winding of transformer.<\/p>\n\n\n\n<p>This parallel path of current is known as excitation branch of equivalent circuit of transformer. The resistive and reactive branches of the excitation circuit can be represented as<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/wp-content\/uploads\/2013\/03\/equivalent-circuit-of-primary-side-of-transformer.gif\" alt=\"equivalent circuit of primary side of transformer\" class=\"wp-image-22358\"\/><\/figure>\n\n\n\n<p><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/machine-equation\/transformer-equation\/equivalent-circuit-of-transformer-referred-to-primary-and-secondary-3.gif\" alt=\"\"><br><br>The load component I<sub>2<\/sub>\u2032 flows through the primary winding of transformer and induced voltage across the winding is E<sub>1<\/sub> as shown in the figure right.<\/p>\n\n\n\n<p>This induced voltage E<sub>1<\/sub> transforms to secondary and it is E<sub>2<\/sub> and load component of primary current I<sub>2<\/sub>\u2032 is transformed to secondary as secondary current I<sub>2<\/sub>. Current of secondary is I<sub>2<\/sub>.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/wp-content\/uploads\/2013\/03\/Equivalent-Circuit-of-Transformer-referred-to-Primary.gif\" alt=\"Equivalent Circuit of Transformer referred to Primary\" class=\"wp-image-22361\"\/><\/figure>\n\n\n\n<p>So the voltage E<sub>2<\/sub> across secondary winding is partly dropped by I<sub>2<\/sub>Z<sub>2<\/sub> or I<sub>2<\/sub>R<sub>2<\/sub> + j.I<sub>2<\/sub>X<sub>2<\/sub> before it appears across load. The load voltage is V<sub>2<\/sub>.<br>The complete equivalent circuit of transformer is shown below.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/wp-content\/uploads\/2013\/03\/Equivalent-Circuit-of-Transformer-referred-to-Primary.gif\" alt=\"Equivalent Circuit of Transformer referred to Primary\" class=\"wp-image-22361\"\/><\/figure>\n\n\n\n<p>Now if we see the voltage drop in secondary from primary side, then it would be \u2032K\u2032 times greater and would be written as K.Z<sub>2<\/sub>.I<sub>2<\/sub>.<br>Again I<sub>2<\/sub>\u2032.N<sub>1<\/sub> = I<sub>2<\/sub>.N<sub>2<\/sub><br><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/machine-equation\/transformer-equation\/equivalent-circuit-of-transformer-referred-to-primary-and-secondary-4.gif\" alt=\"\"><br>Therefore,<br><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/machine-equation\/transformer-equation\/equivalent-circuit-of-transformer-referred-to-primary-and-secondary-5.gif\" alt=\"\"><br>From above equation, secondary impedance of transformer referred to primary is,<br><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/machine-equation\/transformer-equation\/equivalent-circuit-of-transformer-referred-to-primary-and-secondary-6.gif\" alt=\"\"><br>So, the complete equivalent circuit of transformer referred to primary is shown in the figure below:<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Approximate Equivalent Circuit of Transformer<\/h3>\n\n\n\n<p>Since I<sub>o<\/sub> is very small compared to I<sub>1<\/sub>, it is less than 5% of full load primary current, I<sub>o<\/sub> changes the voltage drop insignificantly.<\/p>\n\n\n\n<p>Hence, it is good approximation to ignore the excitation circuit in approximate equivalent circuit of transformer.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/wp-content\/uploads\/2013\/03\/approximate-equivalent-circuit-of-transformer-referred-to-primary.gif\" alt=\"approximate equivalent circuit of transformer referred to primary\" class=\"wp-image-22364\"\/><\/figure>\n\n\n\n<p>The winding resistance and reactance being in series can now be combined into equivalent resistance and reactance of transformer, referred to any particular side. In this case it is side 1 or primary side.<br><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/machine-equation\/transformer-equation\/equivalent-circuit-of-transformer-referred-to-primary-and-secondary-7.gif\" alt=\"\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Equivalent Circuit of Transformer Referred to Secondary<\/h2>\n\n\n\n<p>In a similar way, the approximate equivalent circuit of transformer referred to secondary can be drawn.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/wp-content\/uploads\/2013\/03\/approximate-equivalent-circuit-of-transformer-referred-to-secondary.gif\" alt=\"approximate equivalent circuit of transformer referred to secondary\" class=\"wp-image-22365\"\/><\/figure>\n\n\n\n<p>Where equivalent impedance of transformer referred to secondary, can be derived as<br><img decoding=\"async\" src=\"https:\/\/www.electrical4u.com\/electrical\/machine-equation\/transformer-equation\/equivalent-circuit-of-transformer-referred-to-primary-and-secondary-8.gif\" alt=\"\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the Equivalent Circuit of a Transformer? The equivalent circuit diagram of a transformer is a simplified circuit in which the impedance, resistance and leakage reactance of the transformer can be more easily calculated. The equivalent impedance of transformer is an important parameter to be calculated. This calculation requires the equivalent circuit of transformer [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[450],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/19934"}],"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=19934"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/19934\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=19934"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=19934"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=19934"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}