{"id":2805,"date":"2024-08-25T12:46:16","date_gmt":"2024-08-25T12:46:16","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2805"},"modified":"2024-08-25T12:46:16","modified_gmt":"2024-08-25T12:46:16","slug":"generation-of-three-phase-emfs","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/25\/generation-of-three-phase-emfs\/","title":{"rendered":"GENERATION OF THREE-PHASE EMFS"},"content":{"rendered":"\n

In a three-phase system, there are three equal voltages (or emfs) of the same frequency having a phase difference of 120\u00b0. These voltages can be produced by a three-phase, AC generator having three identical windings (or phases) displaced 120\u00b0 electrical apart. When these windings are rotated in a stationary magnitude field (see Fig. 8.1(a)) or when these windings are kept stationary and the magnetic field is rotated (see Fig. 8.1(b)), an emfs is induced in each winding or phase. These emfs are of same magnitude and frequency, but are displaced from one another by 120\u00b0 electrical.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Fig. 8.1<\/strong>  (a) Coils rotating in stationary magnetic field (b) Magnetic field rotating in stationary coils (c) Wave diagram of induced emfs in three coils (d) Phasor diagram of induced emfs in three coils<\/p>\n\n\n\n

Consider three identical coils a1<\/sub>a2<\/sub>, b1<\/sub>b2<\/sub>, and c1<\/sub>c2<\/sub>\u00a0mounted, as shown in\u00a0Fig 8.1(a)\u00a0and (b). Here, a1<\/sub>, b1<\/sub>, and c1<\/sub>\u00a0are the start terminals, while a2<\/sub>, b2<\/sub>, and c2<\/sub>\u00a0are the finish terminals of the three coils. It may be noted that a phase difference of 120\u00b0 electrical is maintained between the corresponding start terminals a1<\/sub>, b1<\/sub>, and c1<\/sub>. Let the three coils mounted on the same axis be rotated (or the magnetic field system be rotated keeping coils stationary) in anticlockwise direction at\u00a0\u03c9\u00a0<\/em>radians\/s, as shown in\u00a0Figure 8.1(a)\u00a0and\u00a0(b), respectively.<\/p>\n\n\n\n

Three emfs are induced in the three coils, respectively. Their magnitudes and directions, at this instant, are as follows:<\/p>\n\n\n\n

    \n
  1. The emf induced in coil a1<\/sub>a2<\/sub>\u00a0is zero (consider start terminal a1<\/sub>) and is increasing in the positive direction, as shown by wave\u00a0e<\/em>a1a2<\/sub>\u00a0in\u00a0Figure 8.1(c).<\/li>\n\n\n\n
  2. Coil b1<\/sub>b2<\/sub>\u00a0is 120\u00b0 (electrical) behind coil a1<\/sub>a2<\/sub>. The emf induced in this coil is negative and is becoming maximum negative (consider start terminal b1<\/sub>) as shown by\u00a0e<\/em>b1b2<\/sub>\u00a0in\u00a0Figure 8.1(c).<\/li>\n\n\n\n
  3. Coil c1<\/sub>c2<\/sub>\u00a0is 120\u00b0 (electrical) behind b1<\/sub>b2\u00a0<\/sub>or 240\u00b0 (electrical) behind a1<\/sub>a2<\/sub>. The emf induced in this coil is positive and is decreasing (consider start terminal c1<\/sub>) as shown by wave\u00a0e<\/em>c1c2<\/sub>\u00a0in\u00a0Figure 8.1(c).<\/li>\n<\/ol>\n\n\n\n

    <\/a>8.4.1  Phasor Diagram<\/h4>\n\n\n\n

    The emfs induced in three coils are of the same magnitude and frequency, but are displaced by 120\u00b0 (electrical) from each other as shown by phasor diagram in\u00a0Figure 8.1(d). These can be represented by the equations:<\/p>\n\n\n\n

    e<\/em>a1a2<\/sub> = E<\/em>m<\/sub> sin \u03c9t<\/em>; e<\/em>b1b2 <\/sub>= E<\/em>m<\/sub> sin(\u03c9t<\/em> \u2212 2\u03c0<\/em> \/3); e<\/em>c1c2<\/sub> = E<\/em>m<\/sub> sin(\u03c9t<\/em> \u2212 4\u03c0<\/em> \/3) = E<\/em>m<\/sub> sin(\u03c9<\/em> t \u2212 240\u00b0)<\/p>\n","protected":false},"excerpt":{"rendered":"

    In a three-phase system, there are three equal voltages (or emfs) of the same frequency having a phase difference of 120\u00b0. These voltages can be produced by a three-phase, AC generator having three identical windings (or phases) displaced 120\u00b0 electrical apart. When these windings are rotated in a stationary magnitude field (see Fig. 8.1(a)) or […]<\/p>\n","protected":false},"author":1,"featured_media":2806,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[411],"tags":[],"class_list":["post-2805","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-three-phase-ac-circuits"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/download-14.jpeg","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2805","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=2805"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2805\/revisions"}],"predecessor-version":[{"id":2807,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2805\/revisions\/2807"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2806"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2805"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2805"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2805"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}