ELECTRİC DRİVE SYSTEMS AND MATLAB APPLICATIONS

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1 EECTRİC DRİVE SYSTEMS AND MATAB Assist. Pof. D. H. İbahim OKUMUŞ Engineeing Faculty Electical & Electonics Engineeing Depatment (D. Nik Rumzi Nik Idis in des notlaından alınmıştı) 1

2 Contents 1. Intoduction to Electical Dives Rotational Systems, oad couplings, Enegy elationship Quadant opeation Steady-state and dynamic opeation 2. DC moto dives Review of dc motos and chaacteistics Single- and thee-phase thyisto convete cicuits. Tansisto switched-mode convetes. Analysis of convete and dc moto cicuits. Effects of discontinuous conduction on dive. 3. Field oiented contol of induction moto dives Space-vecto epesentation of machine mmfs, voltages, and cuents. Dynamic analysis of the induction moto using the synchonously otating efeence fame; Condition fo alignment of the diect-axis with oto-flux axis. Indiect oto-flux oiented contol stuctue. Effect of oto time-constant on FOC. 2

3 4. Synchonous moto dives Review of synchonous motos and chaacteistics Salient and non-salient pole machines; Reluctance motos Pefomance unde Voltage Souce Invete (VSI) dive Pefomance unde Cuent Souce Invete (CSI) dive oad commutated dive. 5. Application of symmetical component theoy to the opeation of induction motos 5.1 Example of an asymmetical connection (constant voltage type) 5.2 The geneal poblem (phase voltages not constant) 5.3 Connections with line and phase impedances 5.4 Connection with idle phase 6. Opeating anges of the thee phase induction moto 6.1 Plugging 6.2 Motoing 6.3 Induction geneating 3

4 Text Books and Refeences Fo futhe eading, the following books may be consulted: 1. Electic Dives - Ion Boldea, S.A.Nasa, Cc Pess lc, Powe Semiconducto Contolled Dives - G. K. Dubey, Pentice Hall, Fundamentals of Electic Dives M. A. El-Shakawi, Thompson eaning, Electic Machines and Dives G. R. Slemon, Addison Wesley, Powe Electonic Contol of AC Motos J. M. D. Muphy and G. G. Tunbull, Pegamon Pess, Powe Electonics and Moto Dives W. Shephed,. N. Hulley and D. T. W. iang, Cambidge Univesity Pess, 2nd edition, Electic Dives N. Mohan, MNPERE, Minneapolis, USA, Vas P., "Sensoless Vecto and Diect Toque Contol", 1998, Oxfod Univesity Pess 8. Mohan N., Undeland T.M., Robbins W.P., " Powe Electonics; Convetes, Applications and Design", 1995, John Wiley and Sons, Inc. 9. Wildi T., "Electical Machines, Dives, and Powe Systems", 1991, Speika Entepises td. 10. Pillai S.K. "Fist Couse on Electical Dives", 1982, Wiley Easten TD 4

5 11. Hancock N.N, "Elektik Powe Utilization ", 1967, Si Isaac Pitman and Sons td. 12. Bose B.K., "Powe Electonics and AC Dives", 1986, Pintice Hall 13. Subahmanyam V., "Thyisto Contol of Electic Dives", 1986, Tata McGawHill 14. Muphy J.M., "Thyisto Contol of AC Motos", 1973, Pegamon Pess Sen P.C., "Thyisto DC Dives", 1981, John Willey and Sons td. 15. Goss H., "Electical Dives fo Machine Tools", 1983, Siemens 16. Halıcı Kemal, "Elektik Motolai ile Tahik", 1969, Yildiz Univesitesi 17. Unalan E., "Elektikle Tahik", 1967, ITU 18. Kaynak O., "Tah'k Sistemlei", 1986, Bogazici Univesitesi 19. Badu O., "Elektik Kumanda Develei", 1978, MEB Yayini 20. Asik E., "Bantli Konveyole", TMMOB Makine Muhendislei Odasi Yayini (Yayin No:98) 5

6 Desin intenet sitesi: 6

7 Electical Dives Dives ae systems employed fo motion contol Requie pime moves Dives that employ electic motos as pime moves ae known as Electical Dives 7

8 Electical Dives About 50% of electical enegy used fo dives Can be eithe used fo fixed speed o vaiable speed 75% - constant speed, 25% vaiable speed (expanding) MEP 1522 will be coveing vaiable speed dives 8

9 What is a vaiable speed dive? The basic function of a vaiable speed dive (VSD) is to contol the flow of enegy fom the mains to the pocess. To contol the flow of enegy toque and speed theefoe must be contolled. MAINS Toque, Speed Enegy Convesion (Vaiable Speed Dive System) VSD OAD 9

10 Example on VSD application Constant speed Vaiable Speed Dives Supply moto valve pump Powe In Powe out Powe loss Mainly in valve 1 0

11 Example on VSD application Constant speed Vaiable Speed Dives valve Supply moto pump Supply PEC moto pump Powe In Powe out Powe In Powe out Powe loss Mainly in valve Powe loss 1 1

12 Example on VSD application Constant speed Vaiable Speed Dives valve Supply moto pump Supply PEC moto pump Powe In Powe out Powe In Powe out Powe loss Mainly in valve Powe loss 1 2

13 Conventional electic dives (vaiable speed) Bulky Inefficient inflexible 1 3

14 Moden electic dives (With powe electonic convetes) Small Efficient Flexible 1 4

15 Moden electic dives Utility inteface Renewable enegy Machine design Speed sensoless Machine Theoy Inte-disciplinay Seveal eseach aea Expanding Non-linea contol Real-time contol DSP application PFC Speed sensoless Powe electonic convetes 1 5

16 Components in electic dives e.g. Single dive - sensoless vecto contol fom Hitachi 1 6

17 Components in electic dives e.g. Multidives system fom ABB 1 7

18 Components in electic dives Motos DC motos - pemanent magnet wound field AC motos induction, synchonous (IPMSM, SMPSM), bushless DC Applications, cost, envionment Powe souces DC batteies, fuel cell, photovoltaic - unegulated AC Single- thee- phase utility, wind geneato - unegulated Powe pocesso To povide a egulated powe supply Combination of powe electonic convetes Moe efficient Flexible Compact AC-DC DC-DC DC-AC AC-AC 1 8

19 Components in electic dives Contol unit Complexity depends on pefomance equiement analog- noisy, inflexible, ideally has infinite bandwidth. digital immune to noise, configuable, bandwidth is smalle than the analog contolle s DSP/micopocesso flexible, lowe bandwidth - DSPs pefom faste opeation than micopocessos (multiplication in single cycle), can pefom complex estimations 1 9

20 Oveview of AC and DC dives Extacted fom Boldea & Nasa 2 0

21 Oveview of AC and DC dives DC motos: Regula maintenance, heavy, expensive, speed limit Easy contol, decouple contol of toque and flux AC motos: ess maintenance, light, less expensive, high speed Coupling between toque and flux vaiable spatial angle between oto and stato flux 2 1

22 Oveview of AC and DC dives Befoe semiconducto devices wee intoduced (<1950) AC motos fo fixed speed applications DC motos fo vaiable speed applications Afte semiconducto devices wee intoduced (1950s) Vaiable fequency souces available AC motos in vaiable speed applications Coupling between flux and toque contol Application limited to medium pefomance applications fans, blowes, compessos scala contol High pefomance applications dominated by DC motos tactions, elevatos, sevos, etc 2 2

23 Oveview of AC and DC dives Afte vecto contol dives wee intoduced (1980s) AC motos used in high pefomance applications elevatos, tactions, sevos AC motos favoable than DC motos howeve contol is complex hence expensive Cost of micopocesso/semiconductos deceasing pedicted 30 yeas ago AC motos would take ove DC motos 2 3

24 Classification of IM dives (Buja, Kamiekowski, Diect toque contol of PWM invete-fed AC motos - a suvey, IEEE Tansactions on Industial Electonics,

25 Elementay pinciples of mechanics v x Newton s law F m M F f F m F f d Mv dt inea motion, constant M v 2 d d x Fm Ff M M 2 dt dt Ma Fist ode diffeential equation fo speed Second ode diffeential equation fo displacement 2 5

26 Elementay pinciples of mechanics Rotational motion T e, m T l J With constant J, - Nomally is the case fo electical dives T e T l d J dt m T e T l J d dt m J d 2 dt 2 Fist ode diffeential equation fo angula fequency (o velocity) Second ode diffeential equation fo angle (o position) 2 6

27 toque (Nm) EECTRİC DRİVE SYSTEMS AND MATAB speed (ad/s) Elementay pinciples of mechanics Fo constant J, d J dt d dt m m T e d Tl J dt Toque dynamic pesent duing speed tansient Angula acceleation (speed) m The lage the net toque, the faste the acceleation is

28 Elementay pinciples of mechanics Combination of otational and tanslational motions F l M F e T e, T l v F e F l dv M dt T e = (F e ), T l = (F l ), v = T e T l 2 d M dt 2 M - Equivalent moment inetia of the linealy moving mass 2 8

29 Elementay pinciples of mechanics effect of geaing Motos designed fo high speed ae smalle in size and volume ow speed applications use gea to utilize high speed motos Moto T e m oad 1, T l1 m1 n 1 J 2 J 1 n 2 m2 oad 2, T l2 2 9

30 Elementay pinciples of mechanics effect of geaing Moto T e m oad 1, T l1 m1 n 1 J 2 m2 J 1 n 2 oad 2, T l2 Moto T e m Equivalent oad, T lequ J equ J 1 a 2 2 J T lequ = T l1 + a 2 T l2 2 J equ a 2 = n 1 /n 2 3 0

31 SPEED Moto steady state toque-speed chaacteistic Synchonous mch Induction mch Sepaately / shunt DC mch Seies DC TORQUE By using powe electonic convetes, the moto chaacteistic can be change at will 3 1

32 oad steady state toque-speed chaacteistic Fictional toque (passive load) SPEED T~ 2 T~ C T~ Exist in all moto-load dive system simultaneously In most cases, only one o two ae dominating Exists when thee is motion TORQUE Coulomb fiction Viscous fiction Fiction due to tubulent flow 3 2

33 oad steady state toque-speed chaacteistic Constant toque, e.g. gavitational toque (active load) SPEED Gavitational toque Vehicle dive TORQUE T e T gm F T = F = g M sin 3 3

34 oad steady state toque-speed chaacteistic Hoist dive Speed Toque Gavitational toque 3 4

35 oad and moto steady state toque At constant speed, T e = T l Steady state speed is at point of intesection between T e and T l of the steady state toque chaacteistics Toque T e T l Steady state speed Speed 35

36 Toque and speed pofile speed (ad/s) 100 Speed pofile t (ms) The system is descibed by: T e T load = J(d/dt) + B J = 0.01 kg-m2, B = 0.01 Nm/ads-1 and T load = 5 Nm. What is the toque pofile (toque needed to be poduced)? 3 6

37 Toque and speed pofile speed (ad/s) 100 T d J dt B e T l t (ms) 0 < t <10 ms Te = 0.01(0) (0) + 5 Nm = 5 Nm 10ms < t <25 ms Te = 0.01(100/0.015) +0.01( t) + 5 = ( t) Nm 25ms < t< 45ms Te = 0.01(0) (100) + 5 = 6 Nm 45ms < t < 60ms Te = 0.01(-100/0.015) ( t) + 5 = t 3 7

38 Toque and speed pofile speed (ad/s) 100 Speed pofile Toque (Nm) t (ms) toque pofile t (ms)

39 Toque and speed pofile Toque (Nm) 70 J = kg-m2, B = 0.1 Nm/ads-1 and T load = 5 Nm t (ms) -65 Fo the same system and with the moto toque pofile given above, what would be the speed pofile? 3 9

40 Themal consideations Unavoidable powe losses causes tempeatue incease Insulation used in the windings ae classified based on the tempeatue it can withstand. Motos must be opeated within the allowable maximum tempeatue Souces of powe losses (hence tempeatue incease): - Conducto heat losses (i 2 R) - Coe losses hysteesis and eddy cuent - Fiction losses beaings, bush windage 4 0

41 Themal consideations Electical machines can be oveloaded as long thei tempeatue does not exceed the tempeatue limit Accuate pediction of tempeatue distibution in machines is complex hetogeneous mateials, complex geometical shapes Simplified assuming machine as homogeneous body Ambient tempeatue, T o p 1 Input heat powe (losses) Themal capacity, C (Ws/ o C) Suface A, (m 2 ) Suface tempeatue, T ( o C) p 2 Emitted heat powe (convection) 4 1

42 Themal consideations Powe balance: dt C dt p 1 p 2 Heat tansfe by convection: p2 A(T T o ), whee is the coefficient of heat tansfe Which gives: d 1 T dt A T C p C With T(0) = 0 and p 1 = p h = constant, T ph A 1 e t /, whee C A 4 2

43 Themal consideations T p h A ph T A 1 e t / Heating tansient T(0) T t T T(0) e t / Cooling tansient t 4 3

44 Themal consideations The duation of oveloading depends on the modes of opeation: Continuous duty oad toque is constant Continuous ove extended duty peiod multiple Steady state tempeatue Shot eached time intemittent duty Peiodic intemittent duty Nominal output powe chosen equals o exceeds continuous load T p 1n p 1n A osses due to continuous load t 4 4

45 Themal consideations Shot time intemittent duty Opeation consideably less than time constant, Moto allowed to cool befoe next cycle Moto can be oveloaded until maximum tempeatue eached 4 5

46 Themal consideations Shot time intemittent duty p 1s p 1 p1n T p 1s A T max p 1n A t 1 t 4 6

47 Themal consideations Shot time intemittent duty T p p 1s 1n 1 p A1 e p1 n p1s t1/ t 1 / 1n p1s 1 1e e t / A 1 t 1 T max p 1n A T p A 1s t / 1 e t 1 t 4 7

48 Themal consideations Peiodic intemittent duty oad cycles ae epeated peiodically Motos ae not allowed to completely cooled Fluctuations in tempeatue until steady state tempeatue is eached 4 8

49 Themal consideations Peiodic intemittent duty p1 heating coolling heating coolling heating coolling t 4 9

50 Themal consideations Peiodic intemittent duty p Example of a simple case p 1 ectangula peiodic patten p n = 100kW, nominal powe M = 800kg = 0.92, nominal efficiency T = 50 o C, steady state tempeatue ise due to p n 1 p o pn 1 9kW Also, A 180 W / C T 50 1 If we assume moto is solid ion of specific heat c FE =0.48 kws/kg o C, themal capacity C is given by C = c FE M = 0.48 (800) = 384 kws/ o C Finally, themal time constant = /180 = 35 minutes 5 0

51 Themal consideations Peiodic intemittent duty Example of a simple case p 1 ectangula peiodic patten Fo a duty cycle of 30% (peiod of 20 mins), heat losses of twice the nominal, x

52 Toque-speed quadant of opeation 2 T -ve +ve P m -ve T +ve 1 +ve P m +ve T 3 4 T -ve -ve P m +ve T +ve -ve P m -ve 5 2

53 4-quadant opeation m T e m T e Diection of positive (fowad) speed is abitay chosen Diection of positive toque will poduce positive (fowad) speed Quadant 2 Fowad baking Quadant 3 Revese motoing Quadant 1 Fowad motoing Quadant 4 Revese baking T e T m T e m 5 3

54 Ratings of convetes and motos Toque Tansient toque limit Continuous toque limit Powe limit fo tansient toque Powe limit fo continuous toque Maximum speed limit Speed 5 4

55 Steady-state stability 5 5

56 DC MOTOR DRIVES

57 Contents Intoduction Tends in DC dives Pinciples of DC moto dives Modeling of Convetes and DC moto Phase-contolled Rectifie DC-DC convete (Switch-mode) Modeling of DC moto Closed-loop speed contol Cascade Contol Stuctue Closed-loop speed contol - an example Toque loop Speed loop Summay

58 INTRODUCTION DC DRIVES: Electic dives that use DC motos as the pime moves DC moto: industy wokhose fo decades Dominates vaiable speed applications befoe PE convetes wee intoduced Will AC dive eplaces DC dive? Pedicted 30 yeas ago DC stong pesence easy contol huge numbes AC will eventually eplace DC at a slow ate

59 Intoduction DC Motos Advantage: Pecise toque and speed contol without sophisticated electonics Seveal limitations: Regula Maintenance Heavy Spaking Expensive Speed limitations

60 Intoduction DC Motos - 2 pole Roto Stato

61 Intoduction DC Motos - 2 pole Amatue eaction Amatue mmf poduces flux which distots main flux poduce by field X X X X X Mechanical commutato to maintain amatue cuent diection

62 Intoduction Amatue eaction Flux at one side of the pole may satuate Zeo flux egion shifted Flux satuation, effective flux pe pole deceases Amatue mmf distots field flux age machine employs compensation windings and intepoles

63 Intoduction R a a f R f + i a + i f + V t _ e a _ V f _ v t R a i a di a dt e a v f R f i f di f dt Te k t i a Electic toque e a k E Amatue back e.m.f.

64 Intoduction Amatue cicuit: V t R a i a di a dt e a In steady state, V t R k V T t a I a E Theefoe steady state speed is given by, R a a k 2 Thee possible methods of speed contol: Field flux Amatue voltage V t Amatue esistance Ra T T e

65 Intoduction k V T t R a k 2 T T e Vt k T T Vaying V t V t Requies vaiable DC supply T e

66 Intoduction k V T t R a k 2 T T e Vt k T T Vaying V t V t Requies vaiable DC supply T e

67 Intoduction V t (k T ) RaTe k T Vaying V t T Constant T Requies vaiable DC supply T e

68 Intoduction V t V t V t (k T (k ) T ) I RaTe k a T R a Vaying V t V t,ated Constant T I a R a base

69 Intoduction k V T t R a k 2 T T e Vaying R a Vt k T T R a Simple contol osses in extenal esisto T e

70 Intoduction k V T t R a k 2 T T e Vaying Vt k T T Not possible fo PM moto Maximum toque capability educes T e

71 Intoduction Amatue voltage contol : etain maximum toque capability Field flux contol (i.e. flux educed) : educe maximum toque capability Fo wide ange of speed contol 0 to base amatue voltage, above base field flux eduction Amatue voltage contol Field flux contol T e Maximum Toque capability base

72 Intoduction T e Maximum Toque capability base

73 Intoduction P T e Constant toque Constant powe P max base 0 to base amatue voltage, above base field flux eduction P = E a I a,max = k a I a,max P max = E a I a,max = k a base I a,max 1/

74 MODEING OF CONVERTERS AND DC MOTOR POWER EECTRONICS CONVERTERS Used to obtain vaiable amatue voltage Efficient Ideal : lossless Phase-contolled ectifies (AC DC) DC-DC switch-mode convetes(dc DC)

75 Modeling of Convetes and DC moto Phase-contolled ectifie (AC DC) 3-phase supply + V t i a Q2 Q3 Q1 Q4 T

76 Modeling of Convetes and DC moto Phase-contolled ectifie 3- phase supply + V t 3-phase supply Q2 Q3 Q1 Q4 T

77 Modeling of Convetes and DC moto Phase-contolled ectifie 3-phase supply F1 R2 + V a - R1 F2 Q2 Q3 Q1 Q4 T

78 Modeling of Convetes and DC moto Phase-contolled ectifie (continuous cuent) Fiing cicuit fiing angle contol Establish elation between v c and V t i ef + - cuent contolle v c fiing cicuit contolled ectifie + V t

79 Modeling of Convetes and DC moto Phase-contolled ectifie (continuous cuent) Fiing angle contol linea fiing angle contol v t 180 v c v v c t 180 V a 2V m v c cos 180 v t Cosine-wave cossing contol v c v cos s V a 2V m v v c s

80 Modeling of Convetes and DC moto Phase-contolled ectifie (continuous cuent) Steady state: linea gain amplifie Cosine wave cossing method Tansient: sample with zeo ode hold convete T G H (s) T 10 ms fo 1-phase 50 Hz system 3.33 ms fo 3-phase 50 Hz system

81 Modeling of Convetes and DC moto Phase-contolled ectifie (continuous cuent) T d Output voltage Contol signal Cosine-wave cossing T d Delay in aveage output voltage geneation 0 10 ms fo 50 Hz single phase system

82 Modeling of Convetes and DC moto Phase-contolled ectifie (continuous cuent) Model simplified to linea gain if bandwidth (e.g. cuent loop) much lowe than sampling fequency ow bandwidth limited applications ow fequency voltage ipple high cuent ipple undesiable

83 Modeling of Convetes and DC moto Switch mode convetes T1 + V t - Q2 Q3 Q1 Q4 T

84 Switch mode convetes Modeling of Convetes and DC moto T1 T2 D1 D2 + V t - Q2 Q1 Q3 Q4 Q1 T1 and D2 T Q2 D1 and T2

85 Modeling of Convetes and DC moto Switch mode convetes T1 D1 + V t - D3 T3 Q2 Q3 Q1 Q4 T T4 D4 D2 T2

86 Modeling of Convetes and DC moto Switch mode convetes Switching at high fequency Reduces cuent ipple Inceases contol bandwidth Suitable fo high pefomance applications

87 Modeling of Convetes and DC moto Switch mode convetes - modeling + V dc V dc v ti v c q q 1 0 when v c > v ti, uppe switch ON when v c < v ti, lowe switch ON

88 Modeling of Convetes and DC moto Switch mode convetes aveaged model T ti v c q d d 1 T ti t T t ti qdt t T on ti V dc V t V t 1 T ti dt 0 ti V dc dt dv dc

89 Modeling of Convetes and DC moto Switch mode convetes aveaged model d V ti,p 0 V ti,p v c d 0.5 v 2V c ti,p V t 0.5V dc V 2V dc ti,p v c

90 Modeling of Convetes and DC moto Switch mode convetes small signal model V t (s) V 2V dc ti,p v c (s) 2-quadant convete V t (s) V V dc ti,p v c (s) 4-quadant convete

91 Modeling of Convetes and DC moto DC moto sepaately excited o pemanent magnet v t i a R a a di a dt e a T e T l d J dt m T e = k t i a e e = k t Extact the dc and ac components by intoducing small petubations in V t, i a, e a, T e, T and m ac components ~ ~ di v~ dt ~ T ~ k ( i ) a t ia R ~ a a e a e~ e e k E E a ( ~ ) dc components V t I a R T k e a E I E a E e k E a T ~ e T ~ B ~ d( ~ ) J dt T e T B( )

92 Modeling of Convetes and DC moto DC moto small signal model Pefom aplace Tansfomation on ac components ~ ~ di v~ dt a t ia R ~ a a e a V t (s) = I a (s)r a + a sia + E a (s) T ~ e k E ~ ( i a ) T e (s) = k E I a (s) e~ e k E ( ~ ) E a (s) = k E (s) T ~ e T ~ B ~ d( ~ ) J dt T e (s) = T (s) + B(s) + sj(s)

93 Modeling of Convetes and DC moto DC moto small signal model T l (s) (s) Va R a s a - I a (s) T e (s) k 1 (s ) T + B sj k E

94 COSED-OOP SPEED CONTRO Cascade contol stuctue position speed contolle contolle + + * * T* toque contolle convete Moto tacho k T The contol vaiable of inne loop (e.g. toque) can be limited by limiting its efeence value It is flexible oute loop can be eadily added o emoved depending on the contol equiements 1/s

95 COSED-OOP SPEED CONTRO Design pocedue in cascade contol stuctue Inne loop (cuent o toque loop) the fastest lagest bandwidth The oute most loop (position loop) the slowest smallest bandwidth Design stats fom toque loop poceed towads oute loops

96 COSED-OOP SPEED CONTRO Closed-loop speed contol an example OBJECTIVES: Fast esponse lage bandwidth Minimum oveshoot good phase magin (>65 o ) Zeo steady state eo vey lage DC gain BODE POTS METHOD Obtain linea small signal model Design contolles based on linea small signal model Pefom lage signal simulation fo contolles veification

97 COSED-OOP SPEED CONTRO Closed-loop speed contol an example Pemanent magnet moto s paametes Ra = 2 a = 5.2 mh B = 1 x10 4 kg.m 2 /sec k e = 0.1 V/(ad/s) V d = 60 V f s = 33 khz PI contolles J = 152 x 10 6 kg.m 2 k t = 0.1 Nm/A V ti = 5 V Switching signals fom compaison of v c and tiangula wavefom

98 COSED-OOP SPEED CONTRO Toque contolle design v ti q + T c + Toque contolle V dc q k t DC moto T e (s) + - Toque contolle Convete V V dc ti,peak V a (s) R a s a T l (s) I a (s) T (s) k e - 1 (s ) T B sj + k E

99 Phase (deg) Magnitude (db) COSED-OOP SPEED CONTRO Toque contolle design Open-loop gain 150 Bode Diagam Fom: Input Point To: Output Point compensated k pt = 90 k it = compensated Fequency (ad/sec)

100 COSED-OOP SPEED CONTRO Speed contolle design Assume toque loop unity gain fo speed bandwidth << Toque bandwidth * + Speed T* 1 T 1 contolle B sj Toque loop

101 Phase (deg) Magnitude (db) COSED-OOP SPEED CONTRO Speed contolle Open-loop gain 150 Bode Diagam Fom: Input Point To: Output Point 100 k ps = compensated k is = compensated Fequency (Hz)

102 COSED-OOP SPEED CONTRO age Signal Simulation esults Speed Toque

103 COSED-OOP SPEED CONTRO DESIGN EXAMPE SUMMARY Speed contol by: amatue voltage (0 b ) and field flux ( b ) Powe electonics convetes to obtain vaiable amatue voltage Phase contolled ectifie small bandwidth lage ipple Switch-mode DC-DC convete lage bandwidth small ipple Contolle design based on linea small signal model Powe convetes - aveaged model DC moto sepaately excited o pemanent magnet Closed-loop speed contol design based on Bode plots Veify with lage signal simulation

104 EECTRIC DRIVES INDUCTION MOTOR steady-state model (squiel cage)

105 Constuction 120 o c a 120 o b b c a 120 o Stato 3-phase winding Roto squiel cage / wound

106 Constuction Single N tun coil caying cuent i Spans 180 o elec a Pemeability of ion >> o all MMF dop appea in aigap a Ni / 2 -Ni / 2 - -/2 /2

107 Distibuted winding coils ae distibuted in seveal slots Constuction N c fo each slot (3N c i)/2 (N c i)/2 - -/2 /2

108 Distibuted winding (full-pitch) Constuction The esultant MMF is the total contibution of MMF fom each coil Consideing only the space-fundamental component, Concentated Distibuted Distibuted space fundamental Concentated space fundamental

109 Phase a sinusoidal distibuted winding F() Ai gap mmf 2

110 Sinusoidal winding fo each phase poduces space sinusoidal MMF and flux Sinusoidal cuent excitation (with fequency s ) in a phase poduces space sinusoidal standing wave MMF Combination of 3 standing waves esulted in MMF wave otating at: s 2 p 2f p numbe of poles f supply fequency

111

112 Rotating flux induced: emf in stato winding (known as back emf) Emf in oto winding Roto flux otating at synchonous fequency Roto cuent inteact with flux poducing toque Roto AWAYS otate at fequency less than synchonous, i.e. at slip speed: sl = s Ratio between slip speed and synchonous speed known as slip s s s

113 Stato voltage equation: V s = R s I s + j(2f) ls I s + E ag E ag aigap voltage o back emf E ag = k f ag Roto voltage equation: E = R I + js(2f)l E induced emf in oto cicuit E /s = (R / s) I + j(2f)l

114 Pe phase equivalent cicuit + R s ls l I s + + I V s I m m E ag E /s R /s Rs R ls l m s stato winding esistance oto winding esistance stato leakage inductance oto leakage inductance mutual inductance slip

115 We know E g and E elated by The oto paametes efeed to stato ae: E E s Whee a is the winding tun atio g a I a(i '), R R a 2 ', l a l 2 ' oto voltage equation becomes E g = (R / s) I + j(2f) l I

116 Pe phase equivalent cicuit R s I s ls l I + m + R /s V s E ag I m R s R ls l m I stato winding esistance oto winding esistance efeed to stato stato leakage inductance oto leakage inductance efeed to stato mutual inductance oto cuent efeed to stato

117 Powe and Toque Powe is tansfeed fom stato to oto via ai gap, known as aigap powe P ag 3I '2 R s ' 3I '2 R ' 3I '2 R s ' 1 s ost in oto winding Conveted to mechanical powe = (1 s)p ag

118 Powe and Toque Mechanical powe, P m = T em But, s s = s - = (1-s) s P ag = T em s T em P ag s 3I '2 R s s ' Theefoe toque is given by: 3R ' Tem s s R s R ' s 2 V 2 s X X ' 2 ls l

119 Powe and Toque Pull out Toque (T max ) T ated T em T s max m 3 s s R R 2 s s R X X 2 R 2 s ls V 2 s X ls l X l 2 s 0 ated s s m 1 0

120 Steady state pefomance The steady state pefomance can be calculated fom equivalent cicuit, e.g. using Matlab R s I s ls l I + m + R /s V s E ag I m

121 Steady state pefomance R s I s ls l I + m + R /s V s E ag I m e.g. 3 phase squiel cage IM V = 460 V R s = 0.25 R =0.2 = s = 0.5/(2*pi*50) f = 50Hz p = 4 m =30/(2*pi*50)

122 I EECTRİC DRİVE SYSTEMS AND MATAB Is Toque Steady state pefomance

123 Toque Steady state pefomance

124 Efficiency Steady state pefomance (1-s)

125 EECTRIC DRIVES Dynamic Model of Induction Machine

126 WHY NEED DYNAMIC MODE? In an electic dive system, the machine is pat of the contol system elements To be able to contol the dynamics of the dive system, dynamic behavio of the machine need to be consideed Dynamic behavio of of IM can be descibed using dynamic model of IM

127 WHY NEED DYNAMIC MODE? Dynamic model complex due to magnetic coupling between stato phases and oto phases Coupling coefficients vay with oto position oto position vay with time Dynamic behavio of IM can be descibed by diffeential equations with time vaying coefficients

128 Magnetic axis of phase B DYNAMIC MODE, 3-PHASE MODE i bs a c b Magnetic axis of phase A b i as Magnetic axis of phase C i cs a c Simplified equivalent stato winding

129 DYNAMIC MODE 3-phase model stato, b oto, a oto, b stato, a oto, c stato, c

130 DYNAMIC MODE 3-phase model et s look at phase a Flux that links phase a is caused by: Flux poduced by winding a Flux poduced by winding b Flux poduced by winding c

131 DYNAMIC MODE 3-phase model et s look at phase a The elation between the cuents in othe Flux phases poduced and the by winding b flux poduced by these cuents that linked phase a ae Flux poduced by winding c elated by mutual inductances

132 DYNAMIC MODE 3-phase model et s look at phase a as as,s as, as i as abs i bs acs i cs as,a i a as,b i b as,c i c Mutual inductance between phase a and phase b of stato Mutual inductance Mutual inductance between phase Mutual a of inductance Mutual inductance between phase a and stato and phase between a of phase between a of phase a of phase c of oto stato and phase stato b and of phase c of oto Web: oto hiokumus.ktu.edu.t

133 DYNAMIC MODE 3-phase model v abcs = R s i abcs + d( abcs )/dt - stato voltage equation v abc = R i abc + d( abc )/dt - oto voltage equation v abcs v v v as bs cs i abcs i i i as bs cs abcs as bs cs v abc v v v a b c i abc i i i a b c abc a b c abcs flux (caused by stato and oto cuents) that links stato windings abc flux (caused by stato and oto cuents) that links oto windings

134 DYNAMIC MODE 3-phase model abcs abcs,s abcs, abc abc, abc,s Flux linking stato winding due to stato cuent abcs,s as abs acs abs bs bcs acs bcs cs i i i Flux linking stato winding due to oto cuent as bs cs abcs, as,a bs,a cs,a as,b bs,b cs,b as,c bs,c cs,c i i i a b c

135 DYNAMIC MODE 3-phase model Similaly we can wite flux linking oto windings caused by oto and stato cuen Flux linking oto winding due to oto cuent abc, a ab ac ab b bc ac bc c i i i a b c Flux linking oto winding due to stato cuent abc,s a,as b,as c,as a,bs b,bs c,bs a,cs b,cs c,cs i i i as bs cs

136 DYNAMIC MODE 3-phase model The self inductances consist of magnetising and leakage inductances as = ms + ls bs = ms + ls cs = ms + ls The magnetizing inductance ms, accounts fo the flux poduce by the espective phases, cosses the aigap and links othe windings The leakage inductance ls, accounts fo the flux poduce by the espective phases, but does not coss the aigap and links only itself

137 DYNAMIC MODE 3-phase model It can be shown that the magnetizing inductance is given by ms o N 2 s l g 4 It can be shown that the mutual inductance between stato phases is given by: l g 4 2 o abs bcs acs ons cos120 abs bcs acs o N 2 s l g 8 2 ms

138 DYNAMIC MODE 3-phase model The mutual inductances between stato phases (and oto phases) can be witten in tems of magnetising inductances abcs,s ms ms 2 ms 2 ls ms ms 2 ms 2 ls ms ms 2 ms 2 ls i i i as bs cs

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