Outcome of this lecture

Transcription

1 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

2 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

3 tructure of synchronous machines

4 tructure of synchronous machines

5 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.

6 Usage of ifferent types of synch. machines on-salient pole generator High spee (2-4 poles) Large power ( 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

7 3-phase voltage generation imple generator e = F t 400 a 300 e a e b 200 e c inuce voltage (V) a Time (s)

8 Connecting the 3-phase voltages 3 single-phase circuits at ifferent phase angle! Z = ( ) Z = ( ) Z = ( ) = = (2 + )

9 Connecting the 3-phase voltages The potential ifference is known but not the potentials! = ( ) = ( ) = + + =3

10 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

11 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

12 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

13 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

14 tarting the synchronous motor High inertia of the rotor prohibits irect connection into supply net tart as an inuction motor Variable-frequency supply

15 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

16 Equivalent circuit moel orton equivalent circuit I E f f ar = If Xs Xs X 2 = ni re f n = 3 se

17 Determination of synchronous reactance Open circuit test ynchronous spee tator open-circuite Measure V t (I f ) Open-circuit characteristic Air gap line

18 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

19 Unsaturate synchronous reactance Unsaturate value from the air-gap line Ea Zs(unsat) = = Ra + jx I ba s(unsat)

20 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)

21 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

22 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

23 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

24 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

25 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

26 Capability curves Armature heating, length of OM Fiel heating, length of YM teay-state stability

27 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

28 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

29 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

30 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

31 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

32 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

33 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 cos 90 - X X X q

34 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

35 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

36 Permanent Magnet Machine o file control o Fiel current Cost of PM Power factor?

37 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