Outcome of this lecture At the en of this lecture you will be able to: List the ifferent parts of a synchronous machine Explain the operation principles of the machine Use the equivalent circuit moel of the machine Analyze the steay-state operation of the machine Calculate the power transfer of the machine (Torque, power, power factor, etc ) Your will unerstan the ifference between salient pole an non-salient pole machines
Contents of this lecture tructure, construction an use of synchronous machines Infinite bus an synchronization Equivalent circuit of synchronous machine Performance characteristics (torque, power, power factor, etc ) Experimental etermination of reactances alient pole machine phasor iagrams an power transfer
tructure of synchronous machines
tructure of synchronous machines
Main characteristics Rotates at constant spee. Primary energy conversion evices of the wor s electric power system. Both generator an motor operations Can raw either a lagging or a leaing reactive current from the supply.
Usage of ifferent types of synch. machines on-salient pole generator High spee (2-4 poles) Large power (100 1 600 MVA) team power plants alient pole generator Low spee mall an mi-size power (0 800 MVA) Motors for electrical omestic evices Mi size generators for emergency power supply Motors for pumps an ship propulsion Large size generators in hyro-electric power plants
3-phase voltage generation imple generator e = F t 400 a 300 e a e b 200 e c inuce voltage (V) 100 0-100 -200-300 a -400 0 0.01 0.02 0.03 0.04 0.05 0.06 Time (s)
Connecting the 3-phase voltages 3 single-phase circuits at ifferent phase angle! Z = ( ) Z = ( ) Z = ( ) = = (2 + )
Connecting the 3-phase voltages The potential ifference is known but not the potentials! = ( ) = ( ) = + + =3
ynchronous Generators o-loa Excitation voltages Frequency epens on the spee np 120 f f = n = 120 p 2p Ef = f F fkw Ef nf f 2 Open circuit characteristics Magnetization characteristics
ynchronous Generators - loae tator currents establish a rotating fiel in the air-gap Armature reaction flux a Resultant air-gap flux F = F + F r f a
The infinite bus The quasi totality of the electric power generate worlwie is three-phase. Power plants International links ubstations an Transformer Transmission lines Loa centers Inustrial an Resiential loas
Paralleling with the infinite bus ame Voltage Frequency Phase sequence Phase same f an phase sequence same V an phase sequence same V an f
tarting the synchronous motor High inertia of the rotor prohibits irect connection into supply net tart as an inuction motor Variable-frequency supply
Per phase equivalent circuit moel Armature flux, armature reaction flux, armature leakage flux Fa = Far + Fal F = F + F r Er = Ear + Ef - E = jx I E = I jx + E f ar f ( If ) ar ( Ia ) ar a a ar r Magnetizing reactance X ar, (reactance of armature) ynchronous reactance X s =X ar + X al ynchronous impeance Z s =R a + jx s
Equivalent circuit moel orton equivalent circuit I E f f ar = If Xs Xs X 2 = ni re f n = 3 se
Determination of synchronous reactance Open circuit test ynchronous spee tator open-circuite Measure V t (I f ) Open-circuit characteristic Air gap line
Determination of synchronous reactance hort circuit test ynchronous spee tator short-circuite Measure I a (I f ) hort-circuit characteristic traight line Flux remains at low level I a lags E f by almost 90 because
Unsaturate synchronous reactance Unsaturate value from the air-gap line Ea Zs(unsat) = = Ra + jx I ba s(unsat)
aturate synchronous reactance At infinite bus operation the saturation level is efine by terminal voltage operation point c If the fiel current is change the excitation voltage will change along moifie air-gap line OC E = V + I ( R + jx )» V r t a a al t Eca Zs(sat) = = Ra + jx I ba s(sat)
Phasor iagram Terminal voltage taken as the reference vector Generator loa angle positive Motor loa angle negative E = V + I R + I jx = E f t a a a s f V = E + I R + I jx t f a a a s E = V 0 -I R -I jx f t a a a s = E - f Convention: generating current flows out of the machine
Main operation quantities V t = Vt 0 E = E f f Zs = Ra + jxs = Zs qs * t a = VI I * - * * * Ef Vt Ef Vt a = = - * * Ł Zs ł Zs Zs Ef Vt = qs - - qs Z Z s s convention: lagging reactive power positive
Per phase power Complex power Real power P Vt Ef Vt = qs - - qs Z Z s s Vt Ef Vt = cos( qs -) - cosqs Z Z s 2 s 2 Reactive power Q Vt Ef Vt = sin( qs -) - sinqs Z Z s s 2
Power an torque R a neglecte Real power 3 V E P f sin t f 3 = sin = Pmax Xs Reactive power Q Torque T 3f 3Vt Ef 3V = cos - X X s P3f 3 Vt Ef = = sin = T w w X syn syn s t s 2 max sin
Complex power locus 3 V E P f sin t f 3 = sin = Pmax Xs Q 3f 3Vt Ef 3V = cos - X X s t s 2
Capability curves Armature heating, length of OM Fiel heating, length of YM teay-state stability
Power factor control Connecte to an infinite bus P= 3VI t acosf Constant power operation I a cos f = const. jx I = V -E s a t f Reactive current can be controlle by fiel current Also P = 3 VE t f X sin s E f sin = const
Inepenent generators Purely inuctive loa (I sc is short-circuit current) V= E-IX t f a s = X ( I -I ) s sc a Purely resistive loa XI V Ia = t = IR a L R s sc 2 2 L + Xs 2 Vt 2 Ia s sc 2 2 Isc ( X I ) + = 1 quarter ellipse
alient pole machines How reactance is relate to inuctance? What was the efinition of inuctance? Fiel mmf an flux along the -axis ame magnitue of armature mmf prouces more flux in - than in q-irectionłmagnetizing reactance not unique in salient pole machine I a in phase with voltage I a lagging voltage by 90
Two axis ecomposition Armature quantities can be resolve into two components (, I ) ( q, I q ) Components prouce fluxes along respective axes ( a, aq ) -axis armature reactance X q-axis armature reactance X q Leakage reactance X al ynchronous reactances X = Xa + Xal Xq = Xaq + Xal
Phasor Diagrams Component currents (I, I q ) prouce voltage rops (ji X, ji q X q ) E = V + I R + I jx + I jx Ia = I + Iq f t a a q q Generator phasor iagram (I a lagging) y internal power factor angle f terminal power factor angle loa angle R a neglecte
Currents from phasor Diagrams Motoring phasor iagram (I a lagging) y internal power factor angle f terminal power factor angle torque angle V = E + I jx + I jx t f q q y = f I I I = asiny = asin( f ) I = I cosy = I cos( f ) q a a tan = V IX a q IX t a q cosf sinf E = V cos I X f t
Power Transfer * t a = VI = V -( I - ji ) t q * I = E f - V X t cos = V - ( I + ji ) t q I q = V t sin X q 2 2 Vt Vt Ef Vt = sin - + 90 - - cos 90 - X X X q
Power transfer How o you increase the power of a generator? = P + jq Vt Ef P = sin + X 2 Vt ( X -Xq) sin2 2X X q 2 2 Vt Ef 2 sin cos Q= cos - Vt + X X X q if X = X q, then: P = V E t X f sin Vt Ef Q = cos - X V t X 2
Determination of X an X q lip test Rotor riven at small slip Fiel wining open-circuite tator connecte to balance three phase supply tator encounters varying reluctance path Amplitue of the stator current varies What if the rotor is at synch. spee X X q = = i i V t min 2 V t max 2
Permanent Magnet Machine o file control o Fiel current Cost of PM Power factor?
q q q q q q q a) b) c) ) e) f) g) a) surface mounte magnets b) inset rotor with surface magnets c) surface magnets with pole shoes ) embee circumferential magnets e) embee raial magnets f) embee V-magnets with shape air-gap g) permanent magnet assiste synchronous reluctance PM rotor configurations