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<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/625184c074bc5c01059ce537/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">48550 Electrical Energy Technology</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls1 ws1">Chapter 6.</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls2 ws2">Synchronous Machines</div><div class="t m0 x2 h4 y4 ff1 fs2 fc0 sc0 ls3 ws3">Topics to cover:</div><div class="t m0 x2 h5 y5 ff2 fs2 fc0 sc0 ls4 ws4">1) <span class="ls5 ws5">Introduction</span></div><div class="t m0 x2 h5 y6 ff2 fs2 fc0 sc0 ls4 ws4">2) <span class="ls6 ws6">Synchronous machine structures</span></div><div class="t m0 x2 h5 y7 ff2 fs2 fc0 sc0 ls4 ws4">3) <span class="ls7 ws7">Rotating magnetic field</span></div><div class="t m0 x4 h5 y5 ff2 fs2 fc0 sc0 ls4 ws4">4) <span class="ls8 ws8">Equivalent circuit model</span></div><div class="t m0 x4 h5 y6 ff2 fs2 fc0 sc0 ls4 ws4">5) <span class="ls9 ws9">Performance as a generator</span></div><div class="t m0 x4 h5 y7 ff2 fs2 fc0 sc0 ls4 ws4">6) <span class="lsa wsa">Performance as a motor</span></div><div class="t m0 x2 h6 y8 ff1 fs3 fc0 sc0 lsb ws5">Introduction</div><div class="t m0 x5 h7 y9 ff3 fs2 fc0 sc0 lsc wsb">A synchronous machine is an ac rotating machine whose speed under steady state</div><div class="t m0 x2 h7 ya ff3 fs2 fc0 sc0 lsd wsc">condition is proportional to the frequency of the current in its armature. The magnetic field</div><div class="t m0 x2 h7 yb ff3 fs2 fc0 sc0 lse wsd">created by the armature currents rotates at the same speed as that created by the field current</div><div class="t m0 x2 h7 yc ff3 fs2 fc0 sc0 lsf wse">on the rotor, which is rotating at the synchronous speed, and a steady torque results.</div><div class="t m0 x5 h7 yd ff3 fs2 fc0 sc0 ls10 wsf">Synchronous machines are commonly used as generators especially for large power</div><div class="t m0 x2 h7 ye ff3 fs2 fc0 sc0 ls11 ws10">systems, such as turbine generators and hydroelectric generators in the grid power supply.</div><div class="t m0 x2 h7 yf ff3 fs2 fc0 sc0 ls12 ws11">Because the rotor speed is proportional to the frequency of excitation, synchronous motors</div><div class="t m0 x2 h7 y10 ff3 fs2 fc0 sc0 ls13 ws12">can be used in situations where constant speed drive is required. Since the reactive power</div><div class="t m0 x2 h7 y11 ff3 fs2 fc0 sc0 ls14 ws13">generated by a synchronous machine can be adjusted by controlling the magnitude of the</div><div class="t m0 x2 h7 y12 ff3 fs2 fc0 sc0 ls15 ws14">rotor field current, unloaded synchronous machines are also often installed in power systems</div><div class="t m0 x2 h7 y13 ff3 fs2 fc0 sc0 ls16 ws15">solely for power factor correction or for control of reactive <span class="ls17 ws16">kVA flow. Such machines,</span></div><div class="t m0 x2 h7 y14 ff3 fs2 fc0 sc0 ls18 ws17">known as <span class="ff4 ls19 ws18">synchronous condensers</span><span class="ls1a ws19">, may be more economical in the large sizes than static</span></div><div class="t m0 x2 h7 y15 ff3 fs2 fc0 sc0 ls1b ws5">capacitors.</div><div class="t m0 x5 h7 y16 ff3 fs2 fc0 sc0 ls1c ws1a">With power electronic variable voltage variable frequency (VVVF) power supplies,</div><div class="t m0 x2 h7 y17 ff3 fs2 fc0 sc0 ls1d ws1b">synchronous motors, especially those with permanent magnet rotors, are widely used for</div><div class="t m0 x2 h7 y18 ff3 fs2 fc0 sc0 ls1e ws1c">variable speed drives. If the stator excitation of a permanent magnet motor is controlled by</div><div class="t m0 x2 h7 y19 ff3 fs2 fc0 sc0 ls1f ws1d">its rotor position such that the stator field is always 90</div><div class="t m0 x6 h8 y1a ff3 fs4 fc0 sc0 ls20 ws5">o</div><div class="t m0 x7 h7 y19 ff3 fs2 fc0 sc0 ls21 ws1e"> (<span class="ff4 ls22 ws5">electrical</span><span class="lsd ws1f">) ahead of the rotor, the</span></div><div class="t m0 x2 h7 y1b ff3 fs2 fc0 sc0 ls23 ws20">motor performance can be very close to the conventional brushed dc motors, which is very</div><div class="t m0 x2 h7 y1c ff3 fs2 fc0 sc0 ls24 ws21">much favored for variable speed drives. The rotor position can be either detected by using</div><div class="t m0 x2 h7 y1d ff3 fs2 fc0 sc0 ls25 ws22">rotor position sensors or deduced from the induced <span class="ff2 ls26 ws5">emf</span><span class="ls27 ws23"> in the stator windings. Since this</span></div><div class="t m0 x2 h7 y1e ff3 fs2 fc0 sc0 ls28 ws24">type of motors do not need brushes, they are known as <span class="ls29 ws25">brushless dc motors.</span></div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>
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<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/625184c074bc5c01059ce537/bg2.jpg"><div class="t m0 x8 h5 y1f ff2 fs2 fc0 sc0 ls2a ws26">Synchronous Machines</div><div class="t m0 x9 h7 y20 ff3 fs2 fc0 sc0 ls1f ws5">2</div><div class="t m0 x5 h7 y21 ff3 fs2 fc0 sc0 ls2b ws27">In this chapter, we concentrate on conventional synchronous machines whereas the</div><div class="t m0 x2 h7 y22 ff3 fs2 fc0 sc0 ls2c ws28">brushless dc motors will be discussed later in a separate chapter.</div><div class="t m0 x2 h6 y23 ff1 fs3 fc0 sc0 ls2d ws29">Synchronous Machine Structures</div><div class="t m0 x2 h5 y24 ff2 fs2 fc0 sc0 ls2e ws2a">Stator and Rotor</div><div class="t m0 x5 h7 y25 ff3 fs2 fc0 sc0 ls2f ws2b">The armature winding of a conventional synchronous machine is almost invariably on</div><div class="t m0 x2 h7 y26 ff3 fs2 fc0 sc0 ls30 ws2c">the stator and is usually a three phase winding. The field winding is usually on the rotor</div><div class="t m0 x2 h7 y27 ff3 fs2 fc0 sc0 ls31 ws2d">and excited by dc current, or permanent magnets. The dc power supply required for</div><div class="t m0 x2 h7 y28 ff3 fs2 fc0 sc0 ls32 ws2e">excitation usually is supplied through a dc generator known as <span class="ls33 ws2f">exciter, which is often</span></div><div class="t m0 x2 h7 y29 ff3 fs2 fc0 sc0 ls34 ws30">mounted on the same shaft as the synchronous machine. Various excitation systems using</div><div class="t m0 x2 h7 y2a ff3 fs2 fc0 sc0 ls35 ws31">ac <span class="ls36 ws32">exciter and solid state rectifiers are used with large turbine generators.</span></div><div class="t m0 x5 h7 y2b ff3 fs2 fc0 sc0 ls37 ws33">There are two types of rotor structures: <span class="ff4 ls38 ws34">round or</span><span class="ls1f ws35"> <span class="ff4 ls39 ws36">cylindrical rotor and salient pole rotor</span></span></div><div class="t m0 x2 h7 y2c ff3 fs2 fc0 sc0 ls2e ws37">as illustrated schematically in the diagram below. Generally, round rotor structure is used</div><div class="t m0 x2 h7 y2d ff3 fs2 fc0 sc0 ls3a ws38">for high speed synchronous machines, such as steam turbine generators, while salient pole</div><div class="t m0 x2 h7 y2e ff3 fs2 fc0 sc0 ls3b ws39">structure is used for low speed applications, such as hydroelectric generators. The pictures</div><div class="t m0 x2 h7 y2f ff3 fs2 fc0 sc0 ls3c ws3a">below show the stator and rotor of a hydroelectric generator and the rotor of a turbine</div><div class="t m0 x2 h7 y30 ff3 fs2 fc0 sc0 ls3d ws5">generator.</div><div class="t m0 xa h7 y31 ff3 fs2 fc0 sc0 ls3e ws3b">(a) <span class="_ _0"> </span><span class="ls3f ws3c"> (b)</span></div><div class="t m0 xb h7 y32 ff3 fs2 fc0 sc0 lsb ws3d">Schematic illustration of synchronous machines of</div><div class="t m0 xc h7 y33 ff3 fs2 fc0 sc0 ls40 ws3e">(a) round or cylindrical rotor and (b) salient rotor structures</div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>
<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/625184c074bc5c01059ce537/bg3.jpg"><div class="t m0 x8 h5 y1f ff2 fs2 fc0 sc0 ls2a ws26">Synchronous Machines</div><div class="t m0 x9 h7 y20 ff3 fs2 fc0 sc0 ls1f ws5">3</div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>
<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/625184c074bc5c01059ce537/bg4.jpg"><div class="t m0 x8 h5 y1f ff2 fs2 fc0 sc0 ls2a ws26">Synchronous Machines</div><div class="t m0 x9 h7 y20 ff3 fs2 fc0 sc0 ls1f ws5">4</div><div class="t m0 x2 h5 y34 ff2 fs2 fc0 sc0 ls41 ws3f">Angle in Electrical and Mechanical Units</div><div class="t m0 x5 h7 y35 ff3 fs2 fc0 sc0 ls42 ws40">Consider a synchronous machine with two magnetic poles. The idealized radial</div><div class="t m0 x2 h7 y36 ff3 fs2 fc0 sc0 ls43 ws41">distribution of the air gap flux density is sinusoidal along the air gap. When the rotor</div><div class="t m0 x2 h7 y37 ff3 fs2 fc0 sc0 ls44 ws42">rotates for one revolution, the induced <span class="ff2 ls26 ws5">emf</span><span class="ls45 ws43">, which is also sinusoidal, varies for one cycle as</span></div><div class="t m0 x2 h7 y38 ff3 fs2 fc0 sc0 ls46 ws44">illustrated by the <span class="ls47 ws45">waveforms in the diagram below. If we measure the rotor position by</span></div><div class="t m0 x2 h7 y39 ff3 fs2 fc0 sc0 ls48 ws46">physical or mechanical degrees or radians and the phase angles of the flux density and <span class="ls49 ws5">emf</span></div><div class="t m0 x2 h7 y3a ff3 fs2 fc0 sc0 ls4a ws47">by <span class="ff4 ls4b ws48">electrical degrees or radians</span><span class="ls4c ws49">, in this case, it is ready to see that the angle measured in</span></div><div class="t m0 x2 h7 y3b ff3 fs2 fc0 sc0 ls4d ws4a">mechanical degrees or radians is equal to that measured in electrical degrees or radians, i.e.</div><div class="t m0 x2 h9 y33 ff3 fs2 fc0 sc0 ls1f ws35"> <span class="_ _1"> </span><span class="ff5 fs3 ls4e ws5">θ<span class="_ _2"> </span>θ<span class="_ _3"></span><span class="ff6 ls4f">=</span></span></div><div class="t m0 xd ha y3c ff2 fs5 fc0 sc0 ls50 ws5">m</div><div class="t m0 x2 hb y3d ff3 fs2 fc0 sc0 ls51 ws4b">where <span class="ff5 ls52 ws5">θ</span><span class="ls53 ws4c"> is the angle in electrical degrees or radians and <span class="ff5 ls52 ws5">θ</span></span></div><div class="t m0 xe h8 y3e ff3 fs4 fc0 sc0 ls54 ws5">m</div><div class="t m0 xf h7 y3d ff3 fs2 fc0 sc0 ls55 ws4d"> the mechanical angle.</div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>
<div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/625184c074bc5c01059ce537/bg5.jpg"><div class="t m0 x8 h5 y1f ff2 fs2 fc0 sc0 ls2a ws26">Synchronous Machines</div><div class="t m0 x9 h7 y20 ff3 fs2 fc0 sc0 ls1f ws5">5</div><div class="t m0 x10 h7 y3f ff3 fs2 fc0 sc0 ls1f ws35"> </div><div class="t m0 x2 h7 y40 ff3 fs2 fc0 sc0 ls1f ws35"> </div><div class="t m0 x11 hc y41 ff3 fs6 fc1 sc0 ls56 ws5">B(<span class="ff6 ls57">θ</span><span class="ls58">)<span class="_ _4"> </span><span class="ff2 fs7 fc2 ls59">e<span class="_ _5"> </span><span class="ff5 fs6 ls5a">ω<span class="_ _6"> </span></span></span><span class="fc2">)<span class="_ _7"></span>(<span class="_ _8"> </span><span class="ff2 ls5b">t<span class="_ _9"></span><span class="ff3 fc3">&</span></span></span></span></div><div class="t m0 x12 hc y42 ff3 fs6 fc1 sc0 ls56 ws5">B(<span class="ff6 ls57">θ</span><span class="ls58">)</span></div><div class="t m0 x13 hd y43 ff2 fs7 fc2 sc0 ls59 ws5">e<span class="_ _5"> </span><span class="ff5 fs6 ls5a">ω<span class="_ _6"> </span><span class="ff3 ls58">)<span class="_ _7"></span>(<span class="_ _8"> </span><span class="ff2 ls5b">t</span></span></span></div><div class="t m0 x14 he y44 ff5 fs6 fc2 sc0 ls5a ws5">ω<span class="_ _a"></span><span class="ff2 ls5b">t</span></div><div class="t m0 x15 he y45 ff5 fs6 fc1 sc0 ls57 ws5">θ<span class="_ _b"> </span><span class="ff3 fc3 ls5b">&</span></div><div class="t m0 x16 hc y46 ff6 fs6 fc0 sc0 ls5c ws5">π/</div><div class="t m0 x17 hf y47 ff3 fs8 fc0 sc0 ls1f ws5">2</div><div class="t m0 x18 hc y46 ff6 fs6 fc0 sc0 ls5d ws5">π<span class="_ _c"> </span><span class="ls5c">π/<span class="ff3 fs8 ls1f">2</span></span></div><div class="t m0 x19 hf y48 ff3 fs8 fc0 sc0 ls1f ws5">3</div><div class="t m0 x1a hc y46 ff6 fs6 fc0 sc0 ls5d ws5">π<span class="_ _d"></span><span class="ff3 fs8 ls1f">2<span class="_ _e"></span>0</span></div><div class="t m0 x1b hc y49 ff6 fs6 fc0 sc0 ls5d ws5">π<span class="_ _f"> </span>π<span class="_ _d"></span><span class="ff3 fs8 ls1f">2</span></div><div class="t m0 x1c he y4a ff5 fs6 fc1 sc0 ls57 ws5">θ<span class="_ _10"></span><span class="ff3 fs8 fc0 ls5e">m</span></div><div class="t m0 x1d h7 y40 ff3 fs2 fc0 sc0 ls1f ws35"> </div><div class="t m0 x1e hc y4b ff3 fs6 fc1 sc0 ls56 ws5">B(<span class="ff6 ls57">θ</span><span class="ls58">)<span class="_ _4"> </span><span class="ff2 fs7 fc2 ls59">e<span class="_ _5"> </span><span class="ff5 fs6 ls5a">ω<span class="_ _6"> </span></span></span><span class="fc2">)<span class="_ _7"></span>(<span class="_ _8"> </span><span class="ff2 ls5b">t<span class="_ _9"></span><span class="ff3 fc3">&</span></span></span></span></div><div class="t m0 x1f h10 y4c ff3 fs6 fc1 sc0 ls56 ws5">B(</div><div class="t m0 x20 hc y4d ff6 fs6 fc1 sc0 ls57 ws5">θ</div><div class="t m0 x21 h10 y4c ff3 fs6 fc1 sc0 ls58 ws5">)</div><div class="t m0 x22 hd y4e ff2 fs7 fc2 sc0 ls59 ws5">e<span class="_ _5"> </span><span class="ff5 fs6 ls5a">ω<span class="_ _6"> </span><span class="ff3 ls58">)<span class="_ _7"></span>(<span class="_ _8"> </span><span class="ff2 ls5b">t</span></span></span></div><div class="t m0 x23 he y4f ff5 fs6 fc2 sc0 ls5a ws5">ω<span class="_ _a"></span><span class="ff2 ls5b">t</span></div><div class="t m0 x24 he y50 ff5 fs6 fc1 sc0 ls57 ws5">θ<span class="_ _10"> </span><span class="ff3 fc3 ls5b">&</span></div><div class="t m0 x25 hc y46 ff6 fs6 fc0 sc0 ls5d ws5">π<span class="_ _11"> </span>π<span class="_ _d"></span><span class="ff3 fs8 ls1f">2</span></div><div class="t m0 x26 hf y51 ff3 fs8 fc0 sc0 ls1f ws5">0</div><div class="t m0 x27 hc y46 ff6 fs6 fc0 sc0 ls5d ws5">π</div><div class="t m0 x28 hc y51 ff6 fs6 fc0 sc0 ls5d ws5">π<span class="_ _d"></span><span class="ff3 fs8 ls1f">4</span></div><div class="t m0 x29 hf y48 ff3 fs8 fc0 sc0 ls1f ws5">3</div><div class="t m0 x28 hc y52 ff6 fs6 fc0 sc0 ls5d ws5">π<span class="_ _d"></span><span class="ff3 fs8 ls1f">2</span></div><div class="t m0 x2a hc y53 ff6 fs6 fc0 sc0 ls5d ws5">π</div><div class="t m0 x2b he y49 ff5 fs6 fc1 sc0 ls57 ws5">θ</div><div class="t m0 x2c hf y54 ff3 fs8 fc0 sc0 ls5e ws5">m</div><div class="t m0 xa h7 y55 ff3 fs2 fc0 sc0 ls3e ws3b">(a) <span class="_ _0"> </span><span class="ls3f ws3c"> (b)</span></div><div class="t m0 x2d h7 y56 ff3 fs2 fc0 sc0 ls5f ws4e">Flux density distribution in air gap and induced <span class="ff2 ls26 ws5">emf</span><span class="ls22 ws4f"> in the phase</span></div><div class="t m0 x2d h7 y57 ff3 fs2 fc0 sc0 ls60 ws50">winding of a (a) two pole and (b) four pole synchronous machine</div><div class="t m0 x5 h7 y58 ff3 fs2 fc0 sc0 ls61 ws51">A great many synchronous machines have more than two poles. As a specific example,</div><div class="t m0 x2 hb y59 ff3 fs2 fc0 sc0 ls29 ws52">we consider a four pole machine. As the rotor rotates for one revolution (<span class="ff5 ls52 ws5">θ</span></div><div class="t m0 x2e h8 y5a ff3 fs4 fc0 sc0 ls54 ws5">m</div><div class="t m0 x2f h11 y59 ff3 fs2 fc0 sc0 ls62 ws5">=2<span class="ff6 ls63">π</span><span class="ls64 ws53">), the</span></div><div class="t m0 x2 h11 y5b ff3 fs2 fc0 sc0 lsc ws54">induced <span class="ff2 ls26 ws5">emf</span><span class="ls65 ws55"> varies for two cycles (<span class="ff5 ls52 ws5">θ</span><span class="ls62 ws56"> = 4<span class="ff6 ls66 ws5">π</span><span class="ls67 ws57">), and hence</span></span></span></div><div class="t m0 x2 h9 y5c ff3 fs2 fc0 sc0 ls1f ws35"> <span class="_ _1"> </span><span class="ff5 fs3 ls4e ws5">θ<span class="_ _12"> </span>θ<span class="_ _13"></span><span class="ff6 ls4f">=<span class="_"> </span><span class="ff3 ls1f">2</span></span></span></div><div class="t m0 x30 ha y5d ff2 fs5 fc0 sc0 ls50 ws5">m</div><div class="t m0 x5 h7 y5e ff3 fs2 fc0 sc0 ls68 ws58">For a general case, if a machine has <span class="ff2 ls69 ws5">P</span><span class="ls6a ws59"> poles, the relationship between the electrical and</span></div><div class="t m0 x2 h7 y5f ff3 fs2 fc0 sc0 ls1f ws5a">mechanical units of an angle can be readily deduced as</div><div class="t m0 x2 h9 y60 ff3 fs2 fc0 sc0 ls1f ws35"> <span class="_ _1"> </span><span class="ff5 fs3 ls4e ws5">θ<span class="_ _14"> </span>θ<span class="_ _15"></span><span class="ff6 ls4f">=</span></span></div><div class="t m0 x31 h12 y61 ff2 fs3 fc0 sc0 ls6b ws5">P</div><div class="t m0 x32 ha y17 ff2 fs5 fc0 sc0 ls50 ws5">m</div><div class="t m0 x31 h13 y62 ff3 fs3 fc0 sc0 ls1f ws5">2</div><div class="t m0 x5 h7 y63 ff3 fs2 fc0 sc0 ls6c ws5b">Taking derivatives on the both side of the above equation, we obtain</div><div class="t m0 x2 h9 y64 ff3 fs2 fc0 sc0 ls1f ws35"> <span class="_ _1"> </span><span class="ff5 fs3 ls6d ws5">ω<span class="_ _16"> </span>ω<span class="_ _17"></span><span class="ff6 ls4f">=</span></span></div><div class="t m0 x33 h12 y65 ff2 fs3 fc0 sc0 ls6b ws5">P</div><div class="t m0 x34 ha y66 ff2 fs5 fc0 sc0 ls50 ws5">m</div><div class="t m0 x33 h13 y67 ff3 fs3 fc0 sc0 ls1f ws5">2</div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>