{"id":1312,"date":"2026-05-15T20:57:27","date_gmt":"2026-05-15T20:57:27","guid":{"rendered":"https:\/\/www.powersystemsexplained.com\/?page_id=1312"},"modified":"2026-05-15T20:57:28","modified_gmt":"2026-05-15T20:57:28","slug":"synchronous-generators","status":"publish","type":"page","link":"https:\/\/www.powersystemsexplained.com\/?page_id=1312","title":{"rendered":"Synchronous Generators"},"content":{"rendered":"\n<p><strong>What is a synchronous motor<\/strong><\/p>\n\n\n\n<p>A synchronous motor is an AC motor whose rotor rotates at the same speed as the stator\u2019s rotating magnetic field. It uses DC excitation, has no slip, and is ideal for constant\u2011speed, high\u2011efficiency industrial applications.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>Induction Motors vs. Synchronous Motors<\/strong><br>Induction motors and synchronous motors differ mainly in how they operate and how their speed responds to load. An induction motor works through electromagnetic induction: the stator produces a rotating magnetic field that induces current in the rotor, causing it to turn. Because the rotor relies on induced current, it always runs slightly slower than synchronous speed\u2014a difference known as slip, which increases as the load rises. These motors are robust, simple, self starting, and commonly used in applications such as pumps, fans, and conveyors, though they typically run at a lagging power factor.<br>Synchronous motors, on the other hand, use either DC excitation or permanent magnets on the rotor, enabling the rotor to lock into the stator\u2019s rotating magnetic field and run at exact synchronous speed with zero slip, regardless of load. They do not self start and require additional methods, such as a damper cage, or pony motor, to bring the rotor close to synchronous speed before it can lock in. While more complex and expensive, synchronous motors offer high efficiency and the ability to operate at leading, unity, or lagging power factor. With high excitation current, they run at a leading power factor, making them valuable for improving overall industrial power factor.<br>Because the stator immediately produces a rotating magnetic field at energisation, a stationary rotor cannot synchronise with it. The rotor must first be accelerated to near synchronous speed before DC excitation is applied to pull it into synchronism. Once running, the performance of a synchronous motor is mainly influenced by two factors:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Changes in excitation<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Changes in load<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>Example 1<\/strong><\/p>\n\n\n\n<p>A 400V, 8\u2011pole, three\u2011phase, 50\u202fHz star\u2011connected synchronous motor has a stator resistance of 0.40\u202f\u03a9 and a synchronous reactance of 7\u202f\u03a9. When the motor draws 15\u202fA at unity power factor, determine the internally generated EMF and the mechanical load angle.<\/p>\n\n\n\n<p>If the excitation remains unchanged but the load torque is increased so that the current rises to 50\u202fA, determine: <\/p>\n\n\n\n<p>(i)\u2003The new load angle<br>(ii)\u2003The resulting power factor<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"974\" height=\"530\" src=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-39.png\" alt=\"\" class=\"wp-image-1316\" style=\"aspect-ratio:1.8377602297200286;width:712px;height:auto\" srcset=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-39.png 974w, https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-39-300x163.png 300w, https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-39-768x418.png 768w\" sizes=\"auto, (max-width: 974px) 100vw, 974px\" \/><\/figure>\n\n\n\n<p>Note: In a purely inductive load, the angle would be 90 degrees.<\/p>\n\n\n\n<p>The Above could be drawn as follows, which helps with the representation and understanding.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"326\" height=\"299\" src=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-40.png\" alt=\"\" class=\"wp-image-1317\" style=\"aspect-ratio:1.0903134214262313;width:270px;height:auto\" srcset=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-40.png 326w, https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-40-300x275.png 300w\" sizes=\"auto, (max-width: 326px) 100vw, 326px\" \/><\/figure>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>C<\/mi><mi>o<\/mi><mi>s<\/mi><mi>i<\/mi><mi>n<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mi>R<\/mi><mi>u<\/mi><mi>l<\/mi><mi>e<\/mi><mo lspace=\"0.2222em\" rspace=\"0.2222em\">:<\/mo><mtext>&nbsp;<\/mtext><msup><mi>E<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mn>230.9<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mn>105.2<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mn>230.9<\/mn><mo>\u00d7<\/mo><mn>105.2<\/mn><mo>\u00d7<\/mo><mrow><mi>cos<\/mi><mo>\u2061<\/mo><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>86.7<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Cosine\\ Rule: \\ E^2={230.9}^2+{105.2}^2-2\\times230.9\\times105.2\\times\\cos(86.7)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>E<\/mi><mo>=<\/mo><mn>253.2<\/mn><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">E=253.2V\n<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>S<\/mi><mi>i<\/mi><mi>n<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mi>R<\/mi><mi>u<\/mi><mi>l<\/mi><mi>e<\/mi><mo lspace=\"0.2222em\" rspace=\"0.2222em\">:<\/mo><mtext>&nbsp;<\/mtext><mfrac><mn>253.2<\/mn><mrow><mi>S<\/mi><mi>i<\/mi><mi>n<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>86.7<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>105.2<\/mn><mrow><mi>S<\/mi><mi>i<\/mi><mi>n<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03b4<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">Sine\\ Rule:\\ \\frac{253.2}{Sin(86.7)}=\\frac{105.2}{Sin(\\delta)}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>\u03b4<\/mi><mo>=<\/mo><mn>24.5<\/mn><mi>\u00b0<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\delta=24.5\u00b0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>The electrical load angle is the angle of the whole system not per pole, so we have to work it out per pole as shown below:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>M<\/mi><mi>e<\/mi><mi>c<\/mi><mi>h<\/mi><mi>a<\/mi><mi>n<\/mi><mi>i<\/mi><mi>c<\/mi><mi>a<\/mi><mi>l<\/mi><mtext>&nbsp;<\/mtext><mi>L<\/mi><mi>o<\/mi><mi>a<\/mi><mi>d<\/mi><mtext>&nbsp;<\/mtext><mi>A<\/mi><mi>n<\/mi><mi>g<\/mi><mi>l<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mo>=<\/mo><mtext>&nbsp;<\/mtext><mfrac><mrow><mi>E<\/mi><mi>l<\/mi><mi>e<\/mi><mi>c<\/mi><mi>t<\/mi><mi>r<\/mi><mi>i<\/mi><mi>c<\/mi><mi>a<\/mi><mi>l<\/mi><mtext>&nbsp;<\/mtext><mi>L<\/mi><mi>o<\/mi><mi>a<\/mi><mi>d<\/mi><mtext>&nbsp;<\/mtext><mi>A<\/mi><mi>n<\/mi><mi>g<\/mi><mi>l<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03b4<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mrow><mi>P<\/mi><mi>o<\/mi><mi>l<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mi>P<\/mi><mi>a<\/mi><mi>i<\/mi><mi>r<\/mi><mi>s<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>24.5<\/mn><mn>4<\/mn><\/mfrac><mo>=<\/mo><mn>4.08<\/mn><mi>\u00b0<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Mechanical\\ Load\\ Angle\\ =\\ \\frac{Electrical\\ Load\\ Angle\\ (\\delta)}{Pole\\ Pairs}=\\frac{24.5}{4}=4.08\u00b0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p>For this section of the question:<\/p>\n\n\n\n<p>If the excitation remains unchanged but the load torque is increased so that the current rises to 50\u202fA.<\/p>\n\n\n\n<p>If the excitation remains unchanged and the current rises, V<sub>ZS<\/sub> due to IX and IR increasing. But remember that V, Vzs and E need to make a triangle, so if E and V is constant. Vzs must have to pivot up to meet E. But the angle theta must remain the same, which would then make I (the load) start to lag. Therefore, the following must be true.&nbsp;&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"534\" height=\"326\" src=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-42.png\" alt=\"\" class=\"wp-image-1319\" style=\"aspect-ratio:1.6380544811126656;width:437px;height:auto\" srcset=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-42.png 534w, https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-42-300x183.png 300w\" sizes=\"auto, (max-width: 534px) 100vw, 534px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"420\" height=\"439\" src=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-43.png\" alt=\"\" class=\"wp-image-1320\" style=\"aspect-ratio:0.9567204125595665;width:326px;height:auto\" srcset=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-43.png 420w, https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-43-287x300.png 287w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/figure>\n\n\n\n<p>This time we know E!!!<\/p>\n\n\n\n<p>But we only know Theta! As this is the angle from V<sub>zs<\/sub> and I not V.<\/p>\n\n\n\n<p>We have 3 sides and are looking for an angle. So, we can use cosine rule.<\/p>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msup><mn>253.2<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mn>350.6<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mn>230.9<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mn>350.6<\/mn><mo>\u00d7<\/mo><mn>230.9<\/mn><mo>\u00d7<\/mo><mrow><mi>cos<\/mi><mo>\u2061<\/mo><mspace width=\"0.1667em\"><\/mspace><\/mrow><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mi>\u03b3<\/mi><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">{253.2}^2={350.6}^2+{230.9}^2-2\\times350.6\\times230.9\\times\\cos{\\left(\\gamma\\right)}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>\u03b3<\/mi><mo>=<\/mo><mn>46.2<\/mn><mi>\u00b0<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\gamma=46.2\u00b0\n<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>We know <img loading=\"lazy\" decoding=\"async\" width=\"10\" height=\"22\" src=\"data:image\/png;base64,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\">and now <img loading=\"lazy\" decoding=\"async\" width=\"9\" height=\"22\" src=\"data:image\/png;base64,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\">. The phase angle is the angle between V and I, therefore the phase angle can be calculated as follows:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mn>86.7<\/mn><mo>\u2212<\/mo><mn>46.2<\/mn><mo>=<\/mo><mn>40.5<\/mn><mi>\u00b0<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">86.7-46.2=40.5\u00b0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>T<\/mi><mi>h<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mi>P<\/mi><mi>o<\/mi><mi>w<\/mi><mi>e<\/mi><mi>r<\/mi><mtext>&nbsp;<\/mtext><mi>F<\/mi><mi>a<\/mi><mi>c<\/mi><mi>t<\/mi><mi>o<\/mi><mi>r<\/mi><mo>=<\/mo><mi>C<\/mi><mi>o<\/mi><mi>s<\/mi><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mn>40.5<\/mn><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><mo>=<\/mo><mn>0.760<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">The\\ Power\\ Factor=Cos\\left(40.5\\right)=0.760<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mfrac><mn>253.2<\/mn><mrow><mi>S<\/mi><mi>i<\/mi><mi>n<\/mi><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mn>46.2<\/mn><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>350.6<\/mn><mrow><mi>S<\/mi><mi>i<\/mi><mi>n<\/mi><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mi>\u03b4<\/mi><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{253.2}{Sin\\left(46.2\\right)}=\\frac{350.6}{Sin\\left(\\delta\\right)}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>\u03b4<\/mi><mo>=<\/mo><mn>88.0<\/mn><mi>\u00b0<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\delta=88.0\u00b0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>M<\/mi><mi>e<\/mi><mi>c<\/mi><mi>h<\/mi><mi>a<\/mi><mi>n<\/mi><mi>i<\/mi><mi>c<\/mi><mi>a<\/mi><mi>l<\/mi><mtext>&nbsp;<\/mtext><mi>L<\/mi><mi>o<\/mi><mi>a<\/mi><mi>d<\/mi><mtext>&nbsp;<\/mtext><mi>A<\/mi><mi>n<\/mi><mi>g<\/mi><mi>l<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mo>=<\/mo><mtext>&nbsp;<\/mtext><mfrac><mrow><mi>E<\/mi><mi>l<\/mi><mi>e<\/mi><mi>c<\/mi><mi>t<\/mi><mi>r<\/mi><mi>i<\/mi><mi>c<\/mi><mi>a<\/mi><mi>l<\/mi><mtext>&nbsp;<\/mtext><mi>L<\/mi><mi>o<\/mi><mi>a<\/mi><mi>d<\/mi><mtext>&nbsp;<\/mtext><mi>A<\/mi><mi>n<\/mi><mi>g<\/mi><mi>l<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03b4<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mrow><mi>P<\/mi><mi>o<\/mi><mi>l<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mi>P<\/mi><mi>a<\/mi><mi>i<\/mi><mi>r<\/mi><mi>s<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>88<\/mn><mn>4<\/mn><\/mfrac><mo>=<\/mo><mn>22.0<\/mn><mi>\u00b0<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Mechanical\\ Load\\ Angle\\ =\\ \\frac{Electrical\\ Load\\ Angle\\ (\\delta)}{Pole\\ Pairs}=\\frac{88}{4}=22.0\u00b0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p><strong>Example 2<\/strong><\/p>\n\n\n\n<p>A 400V, 8\u2011pole, three\u2011phase, 50\u202fHz star\u2011connected synchronous motor has a stator a synchronous reactance of 7\u202f\u03a9, and the resistance is negligible. When the motor draws 15\u202fA at Leading power factor of 0.78, determine the internally generated EMF and the mechanical load angle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"356\" height=\"466\" src=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-46.png\" alt=\"\" class=\"wp-image-1323\" style=\"aspect-ratio:0.7639872817537792;width:295px;height:auto\" srcset=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-46.png 356w, https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-46-229x300.png 229w\" sizes=\"auto, (max-width: 356px) 100vw, 356px\" \/><\/figure>\n\n\n\n<p>There is no resistance, therefore we know reactance is 90 degrees out of phase. Therefore: <img loading=\"lazy\" decoding=\"async\" width=\"54\" height=\"22\" src=\"data:image\/png;base64,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\"><\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mi>V<\/mi><mrow><mi>Z<\/mi><mi>S<\/mi><\/mrow><\/msub><mo>=<\/mo><mi>I<\/mi><mi>X<\/mi><mo>=<\/mo><mn>15<\/mn><mo>\u00d7<\/mo><mn>7<\/mn><mo>=<\/mo><mn>105<\/mn><mi>V<\/mi><mtext>&nbsp;<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">V_{ZS}=IX=15\\times7=105V\\ <\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>\u03b3<\/mi><mo>=<\/mo><mn>90<\/mn><mo>+<\/mo><mi>\u03d5<\/mi><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mi>P<\/mi><mi>h<\/mi><mi>a<\/mi><mi>s<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mi>a<\/mi><mi>n<\/mi><mi>g<\/mi><mi>l<\/mi><mi>e<\/mi><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><mo>=<\/mo><mn>90<\/mn><mo>+<\/mo><msup><mi>cos<\/mi><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo>\u2061<\/mo><mspace width=\"0.1667em\"><\/mspace><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mn>0.78<\/mn><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><mo>=<\/mo><mn>128.74<\/mn><mi>\u00b0<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\gamma=90+\\phi\\left(Phase\\ angle\\right)=90+\\cos^{-1}{\\left(0.78\\right)}=128.74\u00b0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>C<\/mi><mi>o<\/mi><mi>s<\/mi><mi>i<\/mi><mi>n<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mi>R<\/mi><mi>u<\/mi><mi>l<\/mi><mi>e<\/mi><mo lspace=\"0.2222em\" rspace=\"0.2222em\">:<\/mo><mtext>&nbsp;<\/mtext><msup><mi>E<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mn>230.9<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mn>105<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mn>230.9<\/mn><mo>\u00d7<\/mo><mn>105<\/mn><mo>\u00d7<\/mo><mrow><mi>cos<\/mi><mo>\u2061<\/mo><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>128.74<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Cosine\\ Rule:\\ E^2={230.9}^2+{105}^2-2\\times230.9\\times105\\times\\cos(128.74)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>E<\/mi><mo>=<\/mo><mn>307.71<\/mn><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">E=307.71V<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>S<\/mi><mi>i<\/mi><mi>n<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mi>R<\/mi><mi>u<\/mi><mi>l<\/mi><mi>e<\/mi><mo lspace=\"0.2222em\" rspace=\"0.2222em\">:<\/mo><mfrac><mn>307.71<\/mn><mrow><mi>S<\/mi><mi>i<\/mi><mi>n<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>128.74<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>105<\/mn><mrow><mi>S<\/mi><mi>i<\/mi><mi>n<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03b4<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">Sine\\ Rule: \\frac{307.71}{Sin(128.74)}=\\frac{105}{Sin(\\delta)}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>\u03b4<\/mi><mo>=<\/mo><mn>15.4<\/mn><mi>\u00b0<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\delta=15.4\u00b0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>This is the electrical load angle; to work out the mechanical load angle, we divide by the number of poles pairs.<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>M<\/mi><mi>e<\/mi><mi>c<\/mi><mi>h<\/mi><mi>a<\/mi><mi>n<\/mi><mi>i<\/mi><mi>c<\/mi><mi>a<\/mi><mi>l<\/mi><mtext>&nbsp;<\/mtext><mi>L<\/mi><mi>o<\/mi><mi>a<\/mi><mi>d<\/mi><mtext>&nbsp;<\/mtext><mi>A<\/mi><mi>n<\/mi><mi>g<\/mi><mi>l<\/mi><mi>e<\/mi><mo>=<\/mo><mfrac><mn>15.4<\/mn><mn>4<\/mn><\/mfrac><mo>=<\/mo><mn>3.85<\/mn><mi>\u00b0<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Mechanical\\ Load\\ Angle=\\frac{15.4}{4}=3.85\u00b0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p><strong>Example 3<\/strong><\/p>\n\n\n\n<p>A factory has a load of 500 kVA operating at a lagging power factor of 0.7. A synchronous motor is to be installed to improve the overall power factor to 0.9. When operating, the motor draws 150kW. Determine the required kVA rating of the motor and the power factor at which the motor must operate.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"570\" src=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-50.png\" alt=\"\" class=\"wp-image-1327\" style=\"width:638px;height:auto\" srcset=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-50.png 960w, https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-50-300x178.png 300w, https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-50-768x456.png 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/figure>\n\n\n\n<p>Therefore we know the motors power triangle. We have been given P in the question and now we have worked out the required Q, to increase power factor to 0.9. We just need to workout the motors apparent power and power factor.<\/p>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"556\" height=\"130\" src=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-52.png\" alt=\"\" class=\"wp-image-1329\" style=\"width:316px;height:auto\" srcset=\"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-52.png 556w, https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-52-300x70.png 300w\" sizes=\"auto, (max-width: 556px) 100vw, 556px\" \/><\/figure>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>\u03b8<\/mi><mo>=<\/mo><msup><mrow><mi>t<\/mi><mi>a<\/mi><mi>n<\/mi><\/mrow><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mfrac><mn>188.5<\/mn><mn>150<\/mn><\/mfrac><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><mo>=<\/mo><mn>51.5<\/mn><mi>\u00b0<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\theta={tan}^{-1}\\left(\\frac{188.5}{150}\\right)=51.5\u00b0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mi>F<\/mi><mo>=<\/mo><mi>c<\/mi><mi>o<\/mi><mi>s<\/mi><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mn>51.5<\/mn><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><mo>=<\/mo><mn>0.622<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">PF=cos\\left(51.5\\right)=0.622<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:14px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>S<\/mi><mo>=<\/mo><msqrt><mrow><msup><mn>188.5<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mn>150<\/mn><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><mn>240.9<\/mn><mi>k<\/mi><mi>V<\/mi><mi>A<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">S=\\sqrt{{188.5}^2+{150}^2}=240.9kVA<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:11px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>What is a synchronous motor A synchronous motor is an AC motor whose rotor rotates at the same speed as the stator\u2019s rotating magnetic field. It uses DC excitation, has no slip, and is ideal for constant\u2011speed, high\u2011efficiency industrial applications. Induction Motors vs. Synchronous MotorsInduction motors and synchronous motors differ mainly in how they operate [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"[]"},"class_list":["post-1312","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Synchronous Generators - Power Systems Explained<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.powersystemsexplained.com\/?page_id=1312\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Synchronous Generators - Power Systems Explained\" \/>\n<meta property=\"og:description\" content=\"What is a synchronous motor A synchronous motor is an AC motor whose rotor rotates at the same speed as the stator\u2019s rotating magnetic field. It uses DC excitation, has no slip, and is ideal for constant\u2011speed, high\u2011efficiency industrial applications. 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It uses DC excitation, has no slip, and is ideal for constant\u2011speed, high\u2011efficiency industrial applications. Induction Motors vs. Synchronous MotorsInduction motors and synchronous motors differ mainly in how they operate [&hellip;]","og_url":"https:\/\/www.powersystemsexplained.com\/?page_id=1312","og_site_name":"Power Systems Explained","article_modified_time":"2026-05-15T20:57:28+00:00","og_image":[{"width":974,"height":530,"url":"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-39.png","type":"image\/png"}],"twitter_card":"summary_large_image","twitter_misc":{"Estimated reading time":"8 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.powersystemsexplained.com\/?page_id=1312","url":"https:\/\/www.powersystemsexplained.com\/?page_id=1312","name":"Synchronous Generators - Power Systems Explained","isPartOf":{"@id":"https:\/\/www.powersystemsexplained.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.powersystemsexplained.com\/?page_id=1312#primaryimage"},"image":{"@id":"https:\/\/www.powersystemsexplained.com\/?page_id=1312#primaryimage"},"thumbnailUrl":"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-39.png","datePublished":"2026-05-15T20:57:27+00:00","dateModified":"2026-05-15T20:57:28+00:00","breadcrumb":{"@id":"https:\/\/www.powersystemsexplained.com\/?page_id=1312#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.powersystemsexplained.com\/?page_id=1312"]}]},{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/www.powersystemsexplained.com\/?page_id=1312#primaryimage","url":"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-39.png","contentUrl":"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2026\/05\/image-39.png","width":974,"height":530},{"@type":"BreadcrumbList","@id":"https:\/\/www.powersystemsexplained.com\/?page_id=1312#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.powersystemsexplained.com\/"},{"@type":"ListItem","position":2,"name":"Synchronous Generators"}]},{"@type":"WebSite","@id":"https:\/\/www.powersystemsexplained.com\/#website","url":"https:\/\/www.powersystemsexplained.com\/","name":"Power Systems Explained","description":"The world of electricity","publisher":{"@id":"https:\/\/www.powersystemsexplained.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.powersystemsexplained.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-GB"},{"@type":"Organization","@id":"https:\/\/www.powersystemsexplained.com\/#organization","name":"Power Systems Explained","url":"https:\/\/www.powersystemsexplained.com\/","logo":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/www.powersystemsexplained.com\/#\/schema\/logo\/image\/","url":"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2025\/10\/BannerLogo-2.png","contentUrl":"https:\/\/www.powersystemsexplained.com\/wp-content\/uploads\/2025\/10\/BannerLogo-2.png","width":1605,"height":388,"caption":"Power Systems Explained"},"image":{"@id":"https:\/\/www.powersystemsexplained.com\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/www.powersystemsexplained.com\/index.php?rest_route=\/wp\/v2\/pages\/1312","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.powersystemsexplained.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.powersystemsexplained.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.powersystemsexplained.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.powersystemsexplained.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1312"}],"version-history":[{"count":2,"href":"https:\/\/www.powersystemsexplained.com\/index.php?rest_route=\/wp\/v2\/pages\/1312\/revisions"}],"predecessor-version":[{"id":1333,"href":"https:\/\/www.powersystemsexplained.com\/index.php?rest_route=\/wp\/v2\/pages\/1312\/revisions\/1333"}],"wp:attachment":[{"href":"https:\/\/www.powersystemsexplained.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1312"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}