8. The Synchronous Machine

Transcription

1 8. The Synchronou Machine TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/1 ntitut ür Elektriche

2 Synchronou machine with roun rotor an alient ole rotor ROND ROTOR: Fiel wining itribute in rotor lot; contant air ga SALENT POLE ROTOR: concentrate iel wining on rotor ole; air ga i minimum at ole centre Synchronou machine: Rotor iel wining excite tatic magnetic rotor iel with DC iel current. MOTOR-oeration: Stator 3-hae ac current ytem excite tator rotating air ga iel. Thi iel rotate with n = / an attract rotor magnetic iel, which ha ame number o ole. So rotor will rotate ynchronouly with tator iel. GENERATOR-moe: Rotor i riven mechanically, an inuce with rotor iel in the tator wining a 3-hae voltage ytem with requency = n.. Stator current ue to thi voltage excite tator iel, which rotate ynchronouly with rotor. TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/2 ntitut ür Elektriche

3 Roun rotor ynchronou machine, 8 ole Three iel coil er ole: q r = 3 Damer cage with 9 bar er ole Raial ventilation uct Gla ibre banage or ixing rotor coil overhang Source: VA Tech Hyro, Bhoal, nia TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/3 ntitut ür Elektriche

4 Rotor air ga iel an tator back EMF o roun rotor ynchronou machine Rotor m.m.. an air ga iel itribution have te ue to lot an contain unamental ( = 1): Vˆ Bˆ k k 2 N ( k, k, ) Vˆ, N 0 2 qr N c in W in( / 3) 2 in( / 6), kw k q in( /(6q )), Back EMF (ynchronouly inuce tator voltage): Rotor iel unamental B inuce in 3-hae tator wining at ee n a 3-hae voltage ytem : Examle: q r =2 / 2 Nkw, / 2 2 Nkw, l with requency = n. Current will low in tator wining., 2 r Bˆ r 3 2 k TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/4 ntitut ür Elektriche

5 Roun rotor ynchronou machine: Equivalent circuit Stator wining: Three hae AC wining like in inuction machine with el-inuce voltage ue to tator rotating magnetic iel, ecribe by tator air ga iel main reactance X h an tator leakage lux reactance X. With tator hae reitance R we get tator voltage equation er hae: jx h jx R jx R "ynchronou reactance": iel! X X contain eect o total tator magnetic Equivalent circuit er tator hae: or tator voltage equation (ac voltage an current). n rotor wining only DC voltage an current: R X h h Rotor electric circuit: : Rotor c iel voltage: (exciter voltage): imree via 2 li ring an carbon bruhe a rotor DC current (iel current ) into rotor iel wining. Fiel wining reitance i R. TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/5 ntitut ür Elektriche

6 Traner ratio or rotor iel current Stator el-inuce voltage: by tator air-ga iel Back EMF : nuce by rotor air ga iel. t may be change by iel current arbitrarily DRNG OPERATON = ynchronou machine i controlle voltage ource". a) Amlitue o i etermine via. b) Phae hit o with reect to tator voltage i etermine by relative oition o rotor north ole axi with reect to tator north ole axi. Rotor ole oition i ecribe by loa angle. Amlitue an hae hit o : may be ecribe in equivalent circuit by ictive AC tator current : Thi eine traner ratio o iel current ü : With Vˆ, B B 2 N, k w Vˆ, Vˆ jx Vˆ : h, jx hall _ be h 2 mn 1 ü k w 1 ü we get: ü mnk 2N k w w 2 TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/6 ntitut ür Elektriche

7 h = +jx h Alternative equivalent circuit: Current ource or equivalent iel current h Fictitiou AC current ource generate ynchronou back EMF a voltage ro at magnetizing reactance jx h TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/7 ntitut ür Elektriche

8 Phaor iagram o roun rotor ynchronou machine Examle: Generator, over-excite: a) electrical active ower: P m e Phae angle between -90 an -180 : Hence co negative: P e i negative = ower elivere to the gri (GENERATOR). P e <0: Generator, P e >0: Motor. b) electrical reactive ower: Q m co Phae angle negative = tator current LEADS ahea tator voltage: in negative: Q i negative = caacitive reactive ower: Machine i caacitive conumer. Q < 0: over-excite, caacitive conumer. Q > 0: uner-excite, inuctive conumer. in TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/8 ntitut ür Elektriche

9 Loa angle, internal voltage h, magnetiing current m Loa angle between tator hae voltage an back EMF haor. Counte in mathematical oitive ene (counter-clockwie). nternal voltage h i inuce in tator wining by reulting air ga iel (rotor an tator iel): h jx Magnetiing current m : Fictitiou tator current to excite reulting air ga iel (rotor an tator iel): m Voltage triangle h h an current triangle,, m are o the ame hae, but hite by 90. h, jx, TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/9 ntitut ür Elektriche

10 Loa angle - internal voltage h h Loa angle (exactly at R, X = 0) TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/10 ntitut ür Elektriche

11 Over-/uner-excitation, generator/motor-moe Generator moe: > 0: Rotor LEADS ahea o reulting rotating magnetic iel = Phaor LEADS ahea o h. Motor moe: < 0: Rotor LAGS behin reulting magnetic iel = Phaor LAGS behin h. Over-excitation: Machine i caacitive conumer: Phaor i longer than haor h : big iel current i neee. ner-excitation: Machine i inuctive conumer: Phaor i horter than haor h : mall iel current i neee. Facit: Stator- an rotor iel rotate alway ynchronouly. Generator- an motor moe are only eine by ign o loa angle. TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/11 ntitut ür Elektriche

12 Roun rotor ynchronou machine: Magnetic iel at no-loa Rotor cro ection without iel wining: - Slot er ole 2q r = 10, 2-ole rotor - Rotor may be contructe o maive iron, a rotor contain only tatic magnetic iel! Magnetic iel at no-loa ( = 0, > 0): - Fiel wining excite by - Stator wining without current (no-loa) - Fiel line in air ga in raial irection = no tangential magnetic ull = torque i zero! (Examle: 2 = 2, q = 6, q r = 6) TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/12 ntitut ür Elektriche

13 Roun rotor ynchronou machine: Magnetic iel at loa - Magnetic iel at loa ( > 0, > 0): Rotor ole axi = Direction o, reulting iel axi = Direction o h - Fiel line in air ga have alo tangential comonent = tangential magnetic ull = torque! TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/13 ntitut ür Elektriche

14 Torque o roun rotor ynchronou machine at = cont. & R = 0 Machine oerate at RGD gri: = contant = (= haor ut in real axi o comlex lane): (co j in) an ( ) /( jx ) * ( * ) /( jx ) Active ower P e : P e m P e Re m co m (co jx Re * Electromagnetic torque: j in) m X in (*: conjugate comlex) M e P m yn Pe yn m yn X in M 0 in Note: All loe neglecte ( unity eiciency). Negative torque: Generator: M e i braking Poitive torque: Motor: M e i riving Machine ee i alway ynchronou ee! TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/14 ntitut ür Elektriche

15 Stable oint o oeration Examle: Torque-loa angle curve M(): in generator moe the mechanical riving hat torque M i etermining oeration oint 1 an 2. Oeration oint 1 i table, oeration oint 2 i untable. The tability limit i at loa angle /2 (generator limit) an -/2 (motor limit). Facit: Synchronou motor an generator ull-out torque M 0 occur at ull-out loa angle /2. Rotor i ulle out" o ynchronim, i loa torque excee ull-out torque. Reult: Pulle-out rotor oe not run ynchronouly with tator magnetic iel, which i etermine by the gri voltage. The rotor li! No active ower i converte any longer. TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/15 ntitut ür Elektriche

16 Stability analyi o oeration oint Torque-loa angle curve M e () linearize in oeration oint 0 : Tangent a linearization: with M e( ) M e( 0 ) M e / 0 c ( 0 ) M e / 0 : Equivalent ring contant M e c m Change o loa angle with time caue change o ee : / t ( t) ( t) m m yn NEWTON law o motion: m m J M M c J lea to e( ) ( ) t t 2 2 t J 0 a) / 2 : c c <0, b) / 2 : c c >0 c / 2 2 ( c / J ) 0 0 ( t) ~ in( t) a) : Deviation o loa angle rom teay tate oint o oeration remain limite: STABLE oeration / 2 2 ( c / J ) 0 0 e ( t) ~ inh( t) b) : e m e Deviation o loa angle rom oeration oint increae: NSTABLE e TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/16 ntitut ür Elektriche

17 Torional ocillation o ynchronou machine Deviation o loa angle in table oint o oeration ue to iturbance: / 2 2 ( c / J ) 0 0 ( t) ~ in( t) : e e lea to ierential equation with ocillation a olution. Rotor ocillate aroun teay tate oint o oeration 0,, which i eine by the tator iel, that i generate by the rigi gri. Natural requency o ocillation (eigen-requency): e e 2 Facit: The ynchronou machine i erorming like a (non-linear) torional ring. 1 2 c J Examle: Oeration at no-loa (M e = 0, 0 = 0): With yn = N an rate acceleration time we get: T J c J M N M M yn 0 co( 0) e N T J M M 0 N Synchronou motor riving a an blower or a win tunnel: P N = 50 MW, N = 50 Hz, T J = 10, M 0 /M N = 1.5, e Hz 2 10 TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/17 ntitut ür Elektriche

18 Roun rotor ynchronou machine Stator 1 Turbo- Generator Stator tacking Source: (C) 2007 Bryon Paul McCartney / all right reerve. (C) 2007 Bryon Paul McCartney / all right reerve. TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/18 ntitut ür Elektriche

19 Roun rotor ynchronou machine Stator 2 Turbo- Generator Stator comlete 4-ole Turbogenerator Source: (C) 2007 Bryon Paul McCartney / all right reerve. TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/19 ntitut ür Elektriche

20 Roun rotor ynchronou machine Rotor 1 Turbo- Generator Rotor woun Source: (C) 2007 Bryon Paul McCartney / all right reerve. TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/20 ntitut ür Elektriche

21 Roun rotor ynchronou machine Rotor 2 Turbo- Generator Rotor inertion in tator Source: 4-ole Turbogenerator TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/21 ntitut ür Elektriche

22 Rotor iel an back EMF o alient ole ynchronou machine Bell hae rotor air ga iel curve B (x): A contant m.m.. V excite with a variable air ga (x) a bell hae iel curve. Funamental o thi bell-hae ( = 1): B V ( x) 0 ( x) FORER-unamental wave: Amlitue roortional to Back EMF : Sinuoial rotor iel unamental wave B inuce in three-hae tator wining at ee n a three-hae voltage ytem / 2 Nkw, / 2 2 Nkw, l with requency n Stator current i lowing in tator wining. 2 Bˆ Bˆ TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/22 ntitut ür Elektriche

23 Maive ole reing late Rotor alient ole manuacturing Dove tail rotor ole Lamination ree by reing late Source: VA Tech Hyro, Bhoal, nia TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/23 ntitut ür Elektriche

24 Comlete alient ole ynchronou rotor, 8 ole Fly wheel to increae rotor inertia to limit acceleration in cae o loa ro Shat mounte an with backwar bent raial blae or rotation in clockwie irection at ixe ee Source: VA Tech Hyro, Bhoal, nia Kauli ower lant TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/24 ntitut ür Elektriche

25 Four-ole alient ole rotor with maive ole hoe o aynchronou line tart u a motor - At aynchronou line tart u the tator iel inuce ey current in the rotor maive ole hoe. - Thee ey current evelo with the tator iel the neee tarting torque. 50 Hz, 2 = 4, n = 1500/min Source: VA Tech Hyro, Autria TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/25 ntitut ür Elektriche

26 Salient ole ynchronou machine: Magnetizing inuctance L h Stator wining i three-hae wining like in inuction machine, BT the air ga i LARGER in neutral zone (inter-ole ga o q-axi) than in ole axi (-axi). Hence or equal m.m.. V (inu unamental = 1) the correoning air ga iel i SMALLER in q-axi than in -axi an NOT SNSODAL. Stator iel in -axi (irect axi): Funamental o iel a little bit maller than or contant air ga 0 : ˆ ca. 0.95, thu: c ˆ 1 B / B 1 Stator iel in q-axi (quarature axi): Funamental o iel igniicantly maller than at contant air ga 0 : ˆ ca , thu L c L c q ˆ q 1 B / B 1 L h c L h qh q h TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/26 ntitut ür Elektriche

27 Stator current : - an q-comonent h qh Stator current haor ecomoe into - an q-comonent: i in hae or ooite hae with ictitiou current. So it excite a tator air ga iel in -axi (in rotor ole axi), which together with rotor iel give -axi air ga lux h. q i hae-hite by 90 to an excite thereore a tator air ga iel in q- axi (inter-ole ga). The correoning air ga lux i qh. Stator el-inuce voltage conit o two, by 90 hae hite comonent: j, Lh jlqh q / 2 Lh ( ) h h /( kwn ) an o el-inuce voltage o tator / 2 Lqh q qh qh /( kwn ) leakage lux: j L q TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/27 ntitut ür Elektriche

28 Stator voltage equation o alient ole ynchronou machine Stator voltage equation er hae: Coniering el-inuction o main an leakage lux L h, L qh, L an o rotor hae reitance R we get : R j L j L qh q j L h j L h R j L ( ) j ( L q qh q L h ) X : "ynchronou -axi reactance": X X X h L L h X q : "ynchronou q-axi reactance": X q X X qh L L qh Tyical value: Due to inter-ole ga it i X > X q (tyically: X q = ( ) X ) e.g. alient ole hro-generator, ieel engine generator, reluctance machine,... Note: Roun rotor ynchronou machine may be regare a ecial cae" o alient ole machine or X = X q. The lot oening o rotor iel wining in roun rotor machine may alo be regare a non-contant air ga, yieling alo X > X q (tyically: X q = ( ) X ) TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/28 ntitut ür Elektriche

29 Phaor iagram o laient ole machine Examle: Generator, over-excite: a) an lie in -axi, q lie in q-axi b) ~ j an jx h lie in q-axi, jx qh q lie in -axi (!) nuce internal voltage h : h j h i ecomoe into comonent qh h j L h j L qh qh q Stator voltage an current: - Loa angle, - Phae angle are eine in the ame way a with roun rotor ynchronou machine! h TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/29 ntitut ür Elektriche

30 Torque o alient ole machine at = cont. & R =0 OPERATON at rigi" gri: = contant We chooe: -axi = Re-axi, q-axi = m-axi o comlex lane: j q j q j R = 0: jx jx q q jx X q q j Active ower P e : Electromagnetical torque: P e P e m co m Re m ( X X q ) M e q q P P * m ( ) q m m e q ( X X q ) yn yn yn q q q - Two torque comonent: a) ro. a with roun rotor machine b) "Reluctance torque ue to X. NO rotor excitation i neceary! X q Synchronou reluctance machine: Reluctance torque = robut rotor WTHOT ANY wining, but DEEP inter-ole ga. TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/30 ntitut ür Elektriche

31 jx Torque a unction o loa angle X j q q q j q in j co m M e q ( X X q ) yn m in X X q yn X q X X q M e m X q X q jx in 2 q q in ( 2 1 ( X q 1 X j co )in 2 ) q X q q X TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/31 ntitut ür Elektriche

32 Torque-loa angle curve M e () Torque i exree by tator voltage, back EMF an loa angle:, q are exree by, : M e m X in ( X q 1 X )in 2 Abolute value o ull-out loa angle i < 90, a ull-out torque o reluctance torque occur at loa abgle 45. Pull-out torque i increae by reluctance torque. Equivalent ring contant c bigger than in roun rotor machine, a reluctance torque a ( tier M e ()-curve). TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/32 ntitut ür Elektriche

33 Synchronou reluctance machine Rotor without any wining, but with ee inter-ole ga: X > X q. Rotor -axi want to move into tator iel axi, to allow iel line to cro air ga via the MOST SHORTEST itance oible, thu yieling the reluctance torque. TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/33 ntitut ür Elektriche

34 Salient ole ynchronou machine - Stator Hyro- Generator Stator Source: TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/34 ntitut ür Elektriche

35 Salient ole ynchronou machine - Rotor Hyro- Generator Rotor inertion Three Gorge (China) 840 MVA 80 ole Source: TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/35 ntitut ür Elektriche

36 Hyro Power Plant 1 Hyro- Generator Rotor inertion Three Gorge (China) 840 MVA 80 ole Source: TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/36 ntitut ür Elektriche

37 Hyro Power Plant 2 Hyro- Generator Rotor aembly Karakaya (Turkey) 315 MVA 40 ole Source: TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/37 ntitut ür Elektriche

38 Generator no-loa Rotor with excite iel wining i riven, iel current i 0, tator terminal are not connecte (no tator current low): At oen tator terminal i meaure. jx h 0 TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/38 ntitut ür Elektriche

39 Synchronou machine a hae hiter (R 0) big (over-excite): machine i caacitive conumer R 0 : mall (uner-excite): machine i inuctive conumer Stator connecte to gri, no active ower traner, but hae angle either inuctive or caacitive! jx TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/39 ntitut ür Elektriche

40 Secial oerating oint o ynchronou machine (R 0) h jx non-excite at the gri: = 0. Stator wining current act a magnetizing current R 0 : jx Steay tate hort circuit: Stator wining hort-circuite: = 0, Rotor i riven, i inuce, caue hort circuit current k, which i limite by X an R : k /X R 0 : 0 jx TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/40 ntitut ür Elektriche

41 Synchronou machine in tan-alone oeration Examle: Automotive generator, Air lane / hi generator, generator tation on ilan, o-hore latorm, oai, mountainou region, emergency generator in hoital, military ue (e.g. raar uly) No rigi" gri available: i NOT contant: Rotor i excite an riven, iel current, back EMF i inuce a voltage ource", i eening on loa. E.g.: roun rotor ynchronou machine: No M e ~ in -curve, No rotor ull out at = 90 Examle: Mixe OHM ic-inuctive loa Z L (Loa current L = - ) Loa imeance: Z L (here: Z L = R L + jx L ) TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/41 ntitut ür Elektriche

42 Stan-alone voltage-current characteritic ( ) at R = 0 No-loa: = 0 = = 0 ; Short-circuit: Z L = 0: = 0 = /X = k nuctive loa: Z L jll jx L : Phaor iagram: voltage ro are in line: X Voltage ecreae linear with increaing loa current! / 1 /( / X ) u 1 i Reitive loa: Z L R L : Phaor iagram: right angle triangle. Pythagora: 2 2 ( X ) ( / ) 1 /( / X Voltage-current curve in er-unit o no-loa voltage an hort-circuit current i egment o circle! ) 2 u 2 1 i 2 TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/42 ntitut ür Elektriche

43 Stan-alone oeration: Voltage-current curve ( ) At mixe reitive-inuctive an reitive-caacitive loa the er unit voltage-current curve are ection o ellie. TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/43 ntitut ür Elektriche

44 Stan-alone caacitive loa curve ( ) or R = 0 Caacitive loa: Z L 1/( jcl) jx C : - From haor iagram we ee, that voltage ro are in line! - Two cae are to be coniere: a) in hae ooition to : X C < X CONTER-EXCTATON X / /( / X ) 1 u 1 i jx b) in hae with : X C > X X u 1 i / 1 /( / X ) ually cae b) occur! May alo tart rom un-excite generator, where remanence o rotor inuce a (mall) back EMF in tator wining ( el-excitation o ynchronou generator ). Voltage RSES with increaing loa: FERRANT-henomenon TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/44 ntitut ür Elektriche

45 Examle tan alone oeration: Automotive ynchronou generator Automotive ynchronou generator: three hae, q = 1, ingle layer wave Stator wining woun wining, 12 ole Dioe Stack - Claw ole rotor, electrically excite Sli ring - Driven via belt with variable ee rom internal combution engine - Dioe rectiier or tator ower at 12 V or 24 V DC voltage - Dioe rectiier or rotor iel wining excitation - Tranitor controller kee tator voltage contant - ineenently rom varying ee n an tator loa current via variable exciter current - Data: e. g.: V, 90 A, 1 kw, /min Source: Boch, Germany Claw ole Fan Rotor ring coil a iel wining TECHNSCHE NVERSTÄT Pro. A. Biner : Electrical Machine an Drive 8/45 ntitut ür Elektriche